Skip to main content
SpringerLink
Log in

Finsler Spaces and Their Generalizations

  • Chapter
Book cover Progress in Mathematics

Part of the book series: Progress in Mathematics ((PM,volume 9))

Abstract

Right up to today the ideas of Riemann determine the path of progress in the differential geometry of generalized spaces. These ideas are based on the possibility of the geometrization of the theory of differential invariants relative to some transformation group. This geometrization leans on analogy to the extent that the types of invariants being studied are encountered in the differential geometry of Euclidean space (or of some other Klein space). The generalization consists in the rejection of some relations or others which are characteristic of Klein geometry (in particular, of Euclidean geometry). The first generalization of Riemann geometry (the theory of the invariants of a quadratic differential forfn) is due to Finsler [203, 204] who considered that the square of the arc length element of a curve is an arbitrary homogeneous function of the differentials of the local coordinates of the point. * Certain aspects of Finsler geometry were considered also by Noether [406, 407].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. M. V. Aussem (Vasil’eva), “Metric spaces of n dimensions based on the concept of the area of m-dimensional surfaces,” Uch. Zap. Mosk. Gor. Ped. Inst., Vol. 35, pp. 77–94(1955).

    Google Scholar 

  2. V. I. Bliznikas, “On the theory of curves of a metric line-element space,” Dokl. Akad. Nauk SSSR, 127(1): 9–12 (1959).

    MathSciNet  MATH  Google Scholar 

  3. V.I. Bliznikas, “Congruence of centroidal geodesic curves of a metric line-element space,” Dokl. Akad. Nauk SSSR, 132(4): 735–738 (1960).

    Google Scholar 

  4. V. I. Bliznikas, “On the differential geometry of metric line-element spaces,” Uch. Zap. Vil’nyussk. Gos. Ped. Inst., Vol. 10, pp. 11–29 (1960).

    Google Scholar 

  5. V.I. Bliznikas, “On the differential geometry of bilinear metric line-element spaces,” Vilniaus Univ. Mokslo Darbai, Matem., Fiz., 33(9): 97–106 (1960).

    MathSciNet  Google Scholar 

  6. V.I. Bliznikas, “Certain geometric objects of a metric line-element space,” Liet. Matem. Rinkinys, 1(1–2): 15–23 (1961).

    MathSciNet  MATH  Google Scholar 

  7. V.I. Bliznikas, “Certain aspects of the differential geometry of bilinear metric line-element spaces,” Liet. Matem. Rinkinys, 1(1–2): 372–373 (1961).

    MathSciNet  Google Scholar 

  8. V. I. Bliznikas, “Euclidean connection of Cartan type in a metric line-element space,” Liet. Matem. Rinkinys, 2(2): 33–37 (1963).

    MathSciNet  Google Scholar 

  9. V. I. Bliznikas, “Certain varieties of support elements,” Liet. Matem. Rinkinys, 3(2):221–222 (1963).

    MathSciNet  Google Scholar 

  10. V. I. Bliznikas, “The complete object of a central-projective connection and the torsion-curvature object of a space of central copunctors,” Liet. Matem. Rinkinys, 4(4):457–475 (1964).

    MathSciNet  MATH  Google Scholar 

  11. V. I. Bliznikas, “Affine connection in a support element space,” in: Reports Third Siberian Conf. Math. Mech., 1964, Tomsk Univ., Tomsk (1964), pp. 181–183.

    Google Scholar 

  12. V. I. Bliznikas, “On the theory of curvature of a support element space,” Liet. Matem. Rinkinys, 5(1): 9–24 (1965).

    MathSciNet  MATH  Google Scholar 

  13. V. I. Bliznikas, “Symmetric spaces of central copunctors,” Liet. Matem. Rinkinys, 5(3): 381–389 (1965).

    MathSciNet  MATH  Google Scholar 

  14. V.I. Bliznikas, “Nonholonomic Lie differentiation and linear connections in a support element space,” Liet. Matem. Rinkinys, 6(2): 141–208 (1966).

    MathSciNet  MATH  Google Scholar 

  15. V.I. Bliznikas, “The geometry of normal systems of ordinary higher-order differential equations,” Liet. Matem. Rinkinys, 7(2): 51–68 (1967).

    Google Scholar 

  16. V. I. Bliznikas, “The geometry of systems of second-order partial differential equations,” Liet. Matem. Rinkinys, 7(2): 69–84 (1967).

    Google Scholar 

  17. V. V. Vagner, “A two-dimensional space with a cubic metric,” Uch. Zap. Saratovsk. Gos. Univ., Ser.Fiz.-Mat., Vol. l(XIV), Issue 1, pp. 29–34 (1938).

    Google Scholar 

  18. V. V. Vagner, “Generalized Berwald spaces,” Dokl. Akad. Nauk SSSR, Vol. 39, pp. 3–5 (1943).

    MATH  Google Scholar 

  19. V. V. Vagner, “Two-dimensional Finsler spaces with finite continuous holonomy groups,” Dokl. Akad. Nauk SSSR, Vol. 39, pp. 99–102 (1943).

    Google Scholar 

  20. V. V. Vagner, “The geometry of a space with an areal metric and its application to the calculus of variations,” Mat. Sb., Vol. 19, pp. 341–404 (1946).

    Google Scholar 

  21. V. V. Vagner, “The geometry of an n-dimensional space with an m-dimen-sional Riemann metric and its application to the calculus of variations,” Mat. Sb., Vol. 20, pp. 3–25 (1947).

    MathSciNet  Google Scholar 

  22. V. V. Vagner, “The geometrical interpretation of extremal surfaces in the Lagrange problem for multiple integrals,” Dokl. Akad. Nauk SSSR, Vol. 55, pp. 91–94(1947).

    MathSciNet  MATH  Google Scholar 

  23. V. V. Vagner, “Field theory of local hyperstrips in Xn and its application to the mechanics of a system with nonlinear nonholonomic connections,” Dokl. Akad. Nauk SSSR, 66(6): 1033–1036 (1949).

    MathSciNet  MATH  Google Scholar 

  24. V. V. Vagner, “Finsler geometry as a field theory of local hypersurfaces in Xn,” in: Proc. Seminar Vector Tensor Analysis, Issue 7, pp. 65–166 (1949).

    Google Scholar 

  25. V. V. Vagner, “The geometry of a space with a hyperareal metric as a field theory of local hypersurfaces in a composite variety,” in: Proc. Seminar Vector Tensor Analysis, Issue 8, pp. 144–196 (1950).

    Google Scholar 

  26. V. V. Vagner, “The concept of an indicatrix in the theory of partial differential equations,” Usp. Mat. Nauk, 18(2): 188–189 (1947).

    MathSciNet  Google Scholar 

  27. V. V. Vagner, “The concept of an indicatrix in the theory of differential equations,” Dokl. Akad. Nauk SSSR, Vol. 57, pp. 219–222 (1947).

    MathSciNet  MATH  Google Scholar 

  28. V. V. Vagner, “Geometric theory of the simplest n-dimensional singular problem of the calculus of variations,” Mat. Sb., Vol. 21, pp. 321–364 (1947).

    MathSciNet  Google Scholar 

  29. V. V. Vagner, “The geometry of generalized Cartan spaces and the theory of geometric differential objects,” Dokl. Akad. Nauk SSSR, Vol. 77, pp. 777–780 (1951).

    MathSciNet  MATH  Google Scholar 

  30. V. V. Vagner, “Differential-geometric methods in the calculus of variations,” Uch. Zap. Kazansk. Gos. Univ., 115(10): 4–7 (1955).

    Google Scholar 

  31. V. V. Vagner, “Field theory of local surfaces,” in: Proc. Third All-Union Math. Congr., Vol. 2, Akad. Nauk SSSR, Moscow (1956), pp. 57–60.

    Google Scholar 

  32. V. V. Vagner, “The calculus of variations as a field theory of central semi-cones,” in: Scientific Year Book of Saratov Univ., Mech.-Math. Faculty, 1955, Saratov (1959), pp. 27–34.

    Google Scholar 

  33. A. M. Vasil’ev, “A system of three first-order partial differential equations with three unknown functions and two independent variables (local theory),” Mat. Sb., 70(4): 457–480 (1966).

    MathSciNet  Google Scholar 

  34. A. M. Vasil’ev, “Families of line elements enveloped by completely geodesic families,” Izv. Vysshikh. Uchebn. Zavedenii, Matematika, No. 3, pp. 28–35 (1964).

    Google Scholar 

  35. M. V. Vasil’eva, “The geometry of an integral,” Mat. Sb., 36(1): 57–92(1955).

    MathSciNet  Google Scholar 

  36. M. V. Vasil’eva, “Geometric characteristics of certain invariants of Finsler geometry,” in: Proc. Third All-Union Math. Congr., Vol. 2, Akad. Nauk SSSR, Moscow (1956), p. 139.

    Google Scholar 

  37. M. V. Vasil’eva, “Invariant description of the Cartan geometry of an integral,” Uch. Zap. Mosk. Gos. Ped. Inst. im. V. I. Lenina, No. 208, pp. 76–85 (1963).

    Google Scholar 

  38. M. V. Vasil’eva, “Finsler geometry in an invariant setting,” Uch. Zap. Mosk. Gos. Ped. Inst., No. 243, pp. 38–54 (1965).

    Google Scholar 

  39. M. V. Vasil’eva, “Invariant description of certain Finsler geometries,” Uch. Zap. Mosk. Gos. Ped. Inst., No. 243, pp. 55–68 (1965).

    Google Scholar 

  40. Hsienchu Wei, “Veblen identities in Finsler spaces and in generalized Finsler spaces,” Acta Sci. Nat. Univ. Amoiensis, 12(2): 23–31 (1965).

    Google Scholar 

  41. V. A. Gaukhman, “The geometry of an ordinary second-order differential equation relative to a conformai group of transformations of two variables,” Dokl. Akad. Nauk SSSR, 140(1): 15–18 (1961).

    MathSciNet  Google Scholar 

  42. Chaohao Ku, “Embedding of a Finsler space in a Minkowski space,” Acta Math. Sinica, 6(2): 215–232 (1956).

    MathSciNet  Google Scholar 

  43. Chaohao Ku, “Connection pairs and integral varieties of a system of second-order partial differential equations,” Acta Math. Sinica, 6(3): 426–432 (1956).

    Google Scholar 

  44. Chaohao Ku, “Connection pairs and integral varieties of a system of second-order partial differential equations. I, II,” Acta Math. Sinica, 6(2): 153–162,(1956).

    MathSciNet  Google Scholar 

  45. Chaohao Ku, “Connection pairs and integral varieties of a system of second-order partial differential equations. I, II,” Acta Math. Sinica, 6(2): 163–169(1956).

    Google Scholar 

  46. Chaohao Ku, “Embedding of Finsler varieties in a Minkowski space,” Acta Math. Sinica, 8(2): 272–275 (1958).

    MathSciNet  Google Scholar 

  47. Chaohao Ku and Buchin Su, “First and second variations of a multiple integral in a space with a multiple areal metric,” Acta Math. Sinica, 2(4): 231–245(1953).

    Google Scholar 

  48. L. E. Evtushik, “On the geometry of a double integral,” Mat. Sb., 37(1): 197–208 (1955).

    MathSciNet  Google Scholar 

  49. L. E. Evtushik, Geometry of the integral ∫ F(x α , x n ,x n α , x n αβ )dx 1 … dx n-1], Nauchn. Dokl. Vysshei Shkoly, Fiz.-Mat. Nauk, No. 6, pp. 114–118 (1958).

    Google Scholar 

  50. L. E. Evtushik, “Lie derivative and differential equations of the field of a geometric object,” Dokl. Akad. Nauk, SSSR, 132(5): 998–1001 (1960).

    Google Scholar 

  51. Yu. I. Ermakov, “A three-dimensional space with a cubic semimetric,” Dokl. Akad. Nauk SSSR, 118(6): 1070–1073 (1958).

    MathSciNet  MATH  Google Scholar 

  52. Yu. I. Ermakov, “Spaces Xn with an algebraic metric and a semimetric,” Dokl. Akad. Nauk SSSR, 128(3): 460–463 (1959).

    MathSciNet  MATH  Google Scholar 

  53. G. I. Zhotikov, “On the field theory of local conic surfaces in a first-order tangent composite variety En(Xn), I,” Izv. Vysshikh. Uchebn. Zavedenii, Matematika, No. 3, pp. 53–64(1959).

    Google Scholar 

  54. G.I. Zhotikov, “On the field theory of local surfaces in a first-order tangent composite variety En(Xn),” Izv. Vysshikh. Uchebn. Zavedenii, Matematika, No. 2, pp. 69–79(1959).

    Google Scholar 

  55. G. I. Zhotikov, “On the field theory of local conic surfaces in a first-order tangent composite variety En(Xn). II,” Izv. Vysshikh. Uchebn. Zavedenii, Matematika, No. 4, pp. 64–69 (1959).

    Google Scholar 

  56. G. I. Zhotikov, “On the field theory of local surfaces in a first-order tangent composite variety En(Xn),” in: Proc. Seminar Vector Tensor Analysis, Issue 11, Moscow University (1961), pp. 189–218.

    Google Scholar 

  57. G.I. Zhotikov, “Differential singular Finsler metric defined in Xn by the field of local singular hypersurfaces of singularity class n - m - 1,” Uch. Zap. Bashkirsk. Univ., No. 20, pp. 32–45 (1965).

    Google Scholar 

  58. V.L. Zaguskii, “One form of Finsler space and motions in Minkowski space,” Nauchn. Dokl. Vysshei Shkoly, Fiz.-Mat. Nauk, No. 3, pp. 50–52 (1958).

    Google Scholar 

  59. V. L. Zaguskii, “Certain aspects of Finsler geometry,” Uch. Zap. Yaroslavsk. Gos. Ped. Inst., No. 34, pp. 83–110 (1960).

    Google Scholar 

  60. V.L. Izrailevich, “Invariant characteristics of hypercones in the space W(2,n),” Tr. Saratovsk. Inst. Mekhaniz. S. Kh., No. 26, pp. 211–217 (1963).

    Google Scholar 

  61. V. L Izrailevich, “Theory of cones in the space W(2, n),” in: Works of Young Scientists at Saratov Univ., Math. Sec., Saratov (1964), pp. 37–51.

    Google Scholar 

  62. A. Jonusauskas, “The existence of invariant Finsler metrics in uniform spaces,” Liet. Matem. Rinkinys, 5(1): 45–55 (1965).

    MathSciNet  Google Scholar 

  63. A. Jonusauskas, “The existence of invariant Finsler metrics in uniform spaces with a linear isotropy group of tensory type,” Liet. Matem. Rinkinys, 6(1): 51–57(1966).

    MathSciNet  MATH  Google Scholar 

  64. A. Jonusauskas, “The existence of invariant Finsler metrics in certain uniform spaces,” Liet. Matem. Rinkinys, 6(4): 621–622 (1966).

    MathSciNet  Google Scholar 

  65. N. I. Kabanov, “Geometric theory of Caratheodory transformations in the Lagrange problem,” in: Proc. Seminar Vector Tensor Analysis, Issue 11, Moscow University (1961), pp. 219–240.

    Google Scholar 

  66. N. I. Kabanov, “A Cartan space defined to within Caratheodory transformations,” Uch. Zap. Balashovsk. Gos. Ped. Inst., Vol. 3, pp. 47–77 (1958).

    Google Scholar 

  67. N.I. Kabanov, “A singular Finsler space defined to within Caratheodory transformations,” Sibirsk. Mat. Zh., 2(5): 655–671 (1961).

    MathSciNet  MATH  Google Scholar 

  68. N.I. Kabanov, “On the geometric theory of the simplest singular variational problem for an (n-1)-fold integral,” Dokl. Akad. Nauk SSSR, 140(1): 37–40 (1961).

    MathSciNet  Google Scholar 

  69. N.I. Kabanov, “On the geometric theory of the simplest singular variational problem for an (n-1)-fold integral,” in: Proc. Seminar Vector Tensor Analysis, Issue 12, Moscow University (1963), pp. 239–268.

    Google Scholar 

  70. N.I. Kabanov, “Certain aspects of the geometric theory of Caratheodory transformations in the calculus of variations,” Liet. Matem. Rinkinys, 3(2): 225 (1963).

    MathSciNet  Google Scholar 

  71. F. I. Kagan, “Two-dimensional Finsler spaces admitting of a singular imbedding in a three-dimensional affine space with a vector metric,” Izv. Vysshikh. Uchebn. Zavedenii, Matematika, No. 1, pp. 46–55 (1964).

    Google Scholar 

  72. F. I. Kagan, “An infinitesimal S-extension operation relative to a uniform S-distribution given on Xn,” Volzhsk. Mat. Sb., No. 4, pp. 103–108 (1966).

    Google Scholar 

  73. S.A. Kaganov, “Geometry of a space with a singular hyperareal metric,” Mat. Sb., 42(4):497–512 (1957).

    MathSciNet  Google Scholar 

  74. S.A. Kaganov, “Linear connections in composite varieties defined by a regular hyperareal metric given in Xn,” Sb. Tr. Ufimsk. Neft. Inst., No. 2, pp. 227–286 (1958).

    Google Scholar 

  75. A. T. Kondrat’ev, “Uniform line-element spaces of affine connection A3(x, x) of high mobility,” Volzhsk. Mat. Sb., No. 4, pp. 82–92 (1966).

    Google Scholar 

  76. A. T. Kondrat’ev, “Line-element spaces of affine connection A3(x, x) admitting of an affine motion group Gr (r ≤ 3),” Volzhsk. Mat. Sb., No. 5, pp. 152–157 (1966).

    Google Scholar 

  77. V. K. Kropina, “Projective Finsler spaces with a metric of a certain special form,” Nauchn. Dokl. Vysshei. Shkoly, Fiz.-Mat. Nauk, No. 2, pp. 38–42 (1959).

    Google Scholar 

  78. V. K. Kropina, “Projective Finsler spaces,” Uch. Zap. Arkhang. Gos. Ped. Inst., No. 4, pp. 111–118 (1959).

    Google Scholar 

  79. V. K. Kropina, “The introduction of absolute differentiation in Finsler space,” Uch. Zap. Yaroslavsk. Gos. Ped. Inst., No. 34, pp. 113–123 (1960).

    Google Scholar 

  80. V. K. Kropina, “Projective two-dimensional Finsler spaces with a special metric,” in: Proc. Seminar Vector Tensor Analysis, Issue 11, Moscow University (1961), pp. 277–292.

    Google Scholar 

  81. G. M. Kuz’mina, “The geometry of a system of two partial differential equations,” Uch. Zap. Mosk. Gos. Ped. Inst., No. 243, pp. 99–108 (1965).

    Google Scholar 

  82. B. L. Laptev, “Covariant integration in a Finsler space of two and three dimensions,” Izv. Fiz.-Mat. Obshch., Kazan’, 3(9): 61–76 (1937).

    Google Scholar 

  83. B. L. Laptev, “Lie derivative for objects which are functions of the point and the direction,” Izv. Fiz.-Mat. Obshch., Kazan’, 3(10):3–38 (1938).

    Google Scholar 

  84. B. L. Laptev, “Invariant form of the second variation obtained by Lie differentiation in Finsler space,” Izv. Fiz.-Mat. Obshch., Kazan’, 3(12): 3–8 (1940).

    MathSciNet  Google Scholar 

  85. B. L. Laptev, “Differential invariants of an affinely connected space of tensor support elements,” Uch. Zap. Kazansk. Univ., 116(1): 10–14 (1956).

    MathSciNet  Google Scholar 

  86. B. L. Laptev, “Invariants of a space of tensor support elements,” Uch. Zap. Kazansk. Univ., 115(10): 12 (1955).

    Google Scholar 

  87. B. L. Laptev, “Covariant differential and theory of differential invariants in a space of tensor support elements,” Uch. Zap. Kazansk. Univ., 118(4): 75–147 (1958).

    MathSciNet  MATH  Google Scholar 

  88. B. L. Laptev, “Application of Lie differentiation to the search for the geodesic displacement in a line-element space,” Izv. Vysshikh. Uchebn. Zavedenii, Matematika, No. 2, pp. 173–181 (1958).

    Google Scholar 

  89. B. L. Laptev, “Lie derivative in a support element space,” in: Proc. Seminar Vector Tensor Analysis, Issue 10, Moscow University, pp. 227–248 (1956).

    Google Scholar 

  90. B. L. Laptev, “Lie derivative of geometric objects in a support element space,” Uch. Zap. Kazansk. Univ., 117(2): 16–18 (1957).

    Google Scholar 

  91. B. L. Laptev, “Lie derivative of geometric objects in a support element space,” in: Proc. Third All-Union Math. Congr., Vol. 1, Akad. Nauk SSSR, Moscow (1956), p. 157.

    Google Scholar 

  92. B. L. Laptev, “Support element space,” in: Proc. Fourth All-Union Math. Congr., 1961, Vol. 2, “Nauka,” Leningrad (1964), pp. 221–226.

    Google Scholar 

  93. G. F. Laptev, “Differential geometry of the immersions of varieties. Group-theoretical method of differential-geometric investigations,” Tr. Mosk. Mat. Obshch., No. 2, pp. 275–382 (1953).

    Google Scholar 

  94. G. F. Laptev, “Group-theoretical method of differential-geometric investigations,” in: Proc. Third All-Union Math. Congr., Vol. 2, Akad. Nauk SSSR, Moscow (1956), pp. 60–62.

    Google Scholar 

  95. G. F. Laptev, “Group-theoretical method of differential-geometric investigations,” in: Proc. Third All-Union Math. Congr., Vol. 3, Akad. Nauk SSSR, Moscow (1958), pp. 409–418.

    Google Scholar 

  96. G. F. Laptev, “Varieties immersed in generalized spaces,” in: Proc. Fourth All-Union Math. Congr., 1961, Vol. 2, “Nauka,” Leningrad (1964), pp. 226–233.

    Google Scholar 

  97. G. F. Laptev, “Geometry of differential equations,” in: First All-Union Geometric Conf., Kiev (1962), pp. 6–7.

    Google Scholar 

  98. A. E. Liber, “Two-dimensional spaces with algebraic metric,” in: Proc. Seminar Vector Tensor Analysis, Issue 9, pp. 319–350 (1952).

    Google Scholar 

  99. A. M. Lopshits, “Parallel displacement in spaces with nonquadratic metric,” in: Proc. All-Russian Math. Congr., (1927), pp. 241–242.

    Google Scholar 

  100. M. V. Losik, “Certain class of Kawaguchi spaces,” Dokl. Akad. Nauk SSSR, 134(6): 1299–1302 (1960).

    Google Scholar 

  101. M. V. Losik, “Geometric interpretation of certain conditions in an ordinary variational problem with higher derivatives,” Sibirsk. Mat. Zh., 2(4): 556–566 (1961).

    MathSciNet  MATH  Google Scholar 

  102. M. V. Losik, “A Klein space as a Kawaguchi space,” Dokl. Akad. Nauk SSSR, 139(6): 1299–1301 (1961).

    MathSciNet  Google Scholar 

  103. M. V. Losik, “Kawaguchi spaces connected with Klein spaces,” in: Proc Seminar Vector Tensor Analysis, Issue 12, Moscow University (1963), pp. 213–237.

    Google Scholar 

  104. M. V. Losik, “Connection of Klein spaces with spaces with higher-order areal metric,” in: Works of Young Scientists at Saratov Univ., Math. Sec, Saratov (1964), pp. 55–59.

    Google Scholar 

  105. S. Maziliauskaitė, “Torsion and curvature tensors of the space of central punctors,” Liet. Matem. Rinkinys, 5(3)-.427–433 (1965).

    Google Scholar 

  106. I. H. Medviedevaitė, “Certain aspects of the geometry of a metric space of hyperflat elements,” Liet. Matem. Rinkinys, 6(4): 533–539 (1966).

    Google Scholar 

  107. P. K Rashevskii, “Metric duality in a two-dimensional Finsler geometry, in particular, on an arbitrary surface,” Dokl. Akad. Nauk SSSR, Vol. 3, pp. 147–150 (1935).

    Google Scholar 

  108. P. K. Rashevskii, “Polymetric geometry,” in: Proc. Seminar Vector Tensor Analysis, Issue 5 (1941), pp. 21–147.

    Google Scholar 

  109. N. F. Rzhekhina, “On the field theory of local curves in Xn,” Dokl. Akad. Nauk SSSR, Vol. 72, pp. 461–464 (1950).

    MATH  Google Scholar 

  110. N. F. Rzhekhina, “Field theory of local hypertorses in Xn,” in: Proc. Seminar Vector Tensor Analysis, Issue 9 (1952), pp. 411–430.

    Google Scholar 

  111. N. F. Rzhekhina, “Curves and surfaces in higher-order tangent spaces,” in: Scientific Year Book of Saratov Univ., Mech.-Math. Faculty, 1955, Saratov (1959), pp. 37–38.

    Google Scholar 

  112. Tingchia Hsing, “Symmetry properties in certain Finsler spaces,” Acta Math. Sinica, 9(2): 191–198 (1959).

    MathSciNet  Google Scholar 

  113. N. V. Stepanov, “Geometry of two ordinary second-order differential equations,” Dokl. Akad. Nauk SSSR, 140(1): 62–65 (1961).

    MathSciNet  Google Scholar 

  114. N. V. Stepanov, Classification of pairs of differential equations,Uch. Zap. Velikoluksk. Gos. Ped. Inst., No. 19, pp. 115–116 (1962).

    Google Scholar 

  115. Buchin Su, “Volume geometry of an affinely connected space with an areal metric,” Acta Math. Sinica, 2(4): 246–257 (1953).

    MATH  Google Scholar 

  116. Buchin Su, “Isomorphic transformations of minimal hypersurfaces in Finsler space,” Acta Math. Sinica, 5(4):471–488 (1955).

    MathSciNet  MATH  Google Scholar 

  117. Buchin Su, “What’s new in the geometry of generalized spaces,” Kesyue Tunabao, No. 8, pp. 29–32 (1955).

    Google Scholar 

  118. Buchin Su, “What’s new in the geometry of generalized spaces,” Shusyue Tszin’chzhan’, 1(4): 615–637 (1955).

    Google Scholar 

  119. Buchin Su, “Koschmieder invariant and the associated differential equation of a minimal hypersurface in a regular Cartan space,” Acta Math. Sinica, 6(3): 374–388 (1956).

    MathSciNet  MATH  Google Scholar 

  120. Buchin Su, “Certain affinely connected spaces with an areal metric,” Acta Math. Sinica, 7(2): 285–294 (1957).

    MathSciNet  Google Scholar 

  121. Pênwang Sun, “The equivalence problem for the integral ∫F(x, y, y’,…, y(n)dx,” Acta Math. Sinica, 4(2): 223–224 (1954).

    MathSciNet  Google Scholar 

  122. A. P. Urbonas, “Connections in a support element space,” Liet. Matem. Rinkinys, 6(2): 279–290 (1966).

    MathSciNet  MATH  Google Scholar 

  123. I. Khmelevskii, “Application of the Lie derivative to the search for the extremals in spaces of hyperflat elements,” in: Collection of Aspirants’ Papers at Kazan Univ., Math., Mech., Fiz., Kazan (1964), pp. 94–96.

    Google Scholar 

  124. É. I. Khmelevskii, “Invariant form of the second variation of an (n-1)-fold integral, obtained by Lie differentiation in Cartan space,” in: Collection of Aspirants’ Papers at Kazan Univ., Math., Mech., Fiz., Kazan (1964), pp. 61–68.

    Google Scholar 

  125. I-P’eiCh’en, “A special deformation of a curve in Finsler space,” Acta Sci. Nat. Univ. Amoiensis, 12(2): 123–127 (1965).

    Google Scholar 

  126. Z. N. Chetyrkina, “Homotheties and motions in two-dimensional Finsler spaces,” Volzhsk. Mat. Sb., No. 5, pp. 366–372 (1966).

    Google Scholar 

  127. B. N. Shapukov, “Extremal displacement of a minimal hypersurface in Riemann and Finsler spaces,” Izv. Vysshikh. Uchebn. Zavedenii, Matematika, No. 5, pp. 112–116 (1961).

    Google Scholar 

  128. B. N. Shapukov, “On the theory of bilinear metric spaces,” Uch. Zap. Kazansk. Univ., 123(1): 172–179 (1963).

    Google Scholar 

  129. B. N. Shapukov, “Surfaces and singular paths in a bilinear metric line-element space,” Uch. Zap. Kazansk. Univ., 123(1): 180–195 (1963).

    Google Scholar 

  130. B.N. Shapukov, “On the geometry of bilinear metric line-element space,” in: Collection of Aspirants’ Papers at Kazan Univ., Exact Sciences, Kazan (1962), pp. 158–169.

    Google Scholar 

  131. É. M. Shvartsburd, “Structure equations of a system of four first-order partial differential equations,” Uch. Zap.Mosk.Gos.Ped.Inst., No.243, pp.192–199 (1965).

    Google Scholar 

  132. J. Šinkūnas, “The space of support lineals,” Liet. Matem. Rinkinys, 6(3): 449–455(1966).

    MATH  Google Scholar 

  133. J. Šinkūnas, “Connections in spaces of special support elements,” Liet. Matem. Rinkinys, 6(4): 622 (1966).

    Google Scholar 

  134. A. P. Shirokov, “Gonometric system in Finsler geometry,” in: Proc. Seminar Vector Tensor Analysis, Issue 8 (1950), pp. 414–424.

    Google Scholar 

  135. D. M. Yablokov, “Euclidean connections in the space of pairs of line elements,” in: Proc. Seminar Geom. Dept., Issue 2, Uch. Zap. Kazansk. Univ., Vol. 126, Book 1, pp. 90–102 (1966).

    MATH  Google Scholar 

  136. D. M. Yablokov, “Some applications of Lie differentiation in the space of line element pairs,” in: Proc. Seminar Geom. Dept., Issue 2, Uch. Zap. Kazansk. Univ., Vol. 126, Book 1, pp. 103–116 (1966).

    MATH  Google Scholar 

  137. D. M. Yablokov, “Covariant differentiation and affine connection in a space of line element pairs,” in: Collection of Aspirants’ Papers at Kazan University, Mathematics, Kazan (1966), pp. 80–107.

    Google Scholar 

  138. H. Akbar-Zadeh, “Sur la réductibilité d’une variétés finslériennes” Compt. Rend. Acad. Sci., 234(16): 945–947 (1954).

    MathSciNet  Google Scholar 

  139. H. Akbar-Zadeh, “Sur les isométries infinitésimales d’une variété finslérienn,” Compt. Rend. Acad. Sci., 242(5):608–6l0 (1956).

    MathSciNet  MATH  Google Scholar 

  140. H. Akbar-Zadeh, “Sur une connexion euclidienne d’espace d’éléments linéaires,” Compt. Rend. Acad. Sci., 245(1): 26–28 (1957).

    MathSciNet  MATH  Google Scholar 

  141. H. Akbar-Zadeh, “Sur les espaces de Finsler isotropes,” Compt. Rend. Acad. Sci., 252(14): 2061–2063 (1961).

    MathSciNet  MATH  Google Scholar 

  142. H. Akbar-Zadeh, “Transformations infinitésimales conformes des variétés finslériennes compactes,” Compt. Rend. Acad. Sci., 252(19): 2807–2809 (1961).

    MathSciNet  MATH  Google Scholar 

  143. H. Akbar-Zadeh, “Les espaces de Finsler et certaines de leurs généralisations,” Ann. Sci. Ecole Nom. Supér., 80(1): 1–79 (1963).

    MathSciNet  MATH  Google Scholar 

  144. H. Akbar-Zadeh, “Une généralisation de la géométrie finslérienne,” Cahiers Semin.Topol. et Géom. Différent.Ch. Ehresmann, Fac. Sci. Paris, Vol. 6, pp. 1–9(1964).

    Google Scholar 

  145. H. Akbar-Zadeh, “Sur les automorphismes de certaines structures presque cosymplectiques,” Can. Math. Bull., 8(1):39–57 (1965).

    MathSciNet  MATH  Google Scholar 

  146. H. Akbar-Zadeh, “Sur les homothétiew infinitésimales des variétés finslér-iennes,” Compt. Rend. Acad. Sci., AB262(19): A1058–A1060 (1966).

    MathSciNet  Google Scholar 

  147. H. Akbar-Zadeh and E. Bonan, “Structure presque kahlérienne naturelle sur le fibré tengent à une variété finslérienne,” Compt. Rend. Acad. Sci., 258(23): 5581–5582 (1964).

    MathSciNet  MATH  Google Scholar 

  148. F. Alardin, “L’autoparallélisme des courbes extrémales dans les espaces métriques fondés sur la notion d’aire,” J. Math. Pures et Appl., 9(27): 255–336 (1948).

    MathSciNet  Google Scholar 

  149. N. Aronszajn, “Sur quelques problèmes concernant les espaces de Minkowski et les espaces vectorièls généraux,” Atti Accad. Naz. Lincei, Rend., 6(26): 374–376 (1937).

    Google Scholar 

  150. L. Auslander, “On curvature in Finsler Geometry,” Trans. Am. Math. Soc, 79(2): 378–388 (1955).

    MathSciNet  MATH  Google Scholar 

  151. O. Bark, “On the projective connection space and general projective geometry of paths,” Kyungpook Math. J., Vol. 1, pp. 1–12 (1958).

    MathSciNet  Google Scholar 

  152. W. Barthel, “Über eine Parallelverschiebung mit Längeninvarianz in lokal-Minkowskischen Räumen. I, II,” Arch. Math., 4(4): 346–354 (1953).

    MathSciNet  MATH  Google Scholar 

  153. W. Barthel, “Über Minkowskische und Finslersche Geometrie,” in: Convegno Internationale di Geometria Differenziele, Italia, 1953, Ed. Gremonese, Rome (1954), pp. 71–76.

    Google Scholar 

  154. W. Barthel, “Zur Flächentheorie in Finslerschen Räumen,” in: Proc. Internat. Congr. Math., 1954, Amsterdam (1954), pp. 194–196.

    Google Scholar 

  155. W. Barthel., “Über die Minimalflächen in gefäserten Finslerräumen,” Ann. Mat. Pura ed Appl., Vol. 36, pp. 159–190 (1954).

    MathSciNet  MATH  Google Scholar 

  156. W. Barthel, “Über das Verhältnis der Vektoräbertragung zu den Variationsproblemen in Cartanschen Raümen,” Rend. Circolo Mat. Palarmo, 3(2): 270–3(2): 270–281 (1954).

    MathSciNet  MATH  Google Scholar 

  157. W. Barthel, “Zur Flächentheorie in Finslerschen Räumen,” in: Proc. Internat. Congr. Math., Amsterdam (1954), p. 2;

    Google Scholar 

  158. W. Barthel, “Zur Flächentheorie in Finslerschen Räumen,” Math. Z., 62(1): 23–26 (1955).

    MathSciNet  MATH  Google Scholar 

  159. W. Barthel, “Über metrische Differentialgeometrie, begründet auf dem Begriff eines p-dimensionalen Areals,” Math. Ann., 137(1): 42–63 (1959).

    MathSciNet  MATH  Google Scholar 

  160. W. Barthel, “Zur Minkowski-Geometrie, begründet auf dem Flächeninhaltsbegriff,” Monatsh. Math., 63(4): 217–343 (1959).

    MathSciNet  Google Scholar 

  161. R. Behari and N. Prakash, “A study of normal curvature of a vector field in Minkowskian Finsler space,” J. Indian Math. Soc., 24(3–4):443–456[1960 (1961)].

    MathSciNet  MATH  Google Scholar 

  162. L. Berwald, “Untersuchung der Krümmung allgemeiner metrischer Räume auf Grund des in ihnen herrschenden Parallelismus,” Math. Z., 25:40–73 (1926).

    MathSciNet  MATH  Google Scholar 

  163. L. Berwald, “On the projective geometry of paths,” Ann. Math., 37: 879–898 (1936).

    MathSciNet  Google Scholar 

  164. L. Berwald, “Über Finslersche und Cartansche Geometrie. I. Geometriesche Erklärungen der Krümmung und des Hauptskalers im zweidimensionalen Finslerschen Raum,” Mathematica, Timisoara, 17:34–55 (1941).

    MathSciNet  Google Scholar 

  165. L. Berwald, “Über Finslersche und Cartansche Geometrie. II. Invarianten bei der Variation vielfachen Integrale und Parallelhyperflächen in Cartanschen Räumen,” Compositio Math., 7:141–176 (1939).

    MathSciNet  MATH  Google Scholar 

  166. L. Berwald, “On the Finsler and Cartan geometry. III. Two-dimensional Finsler spaces with rectilinear extrem als,” Ann. Math., Ser. 2,42:84–112 (1941).

    MathSciNet  Google Scholar 

  167. L. Berwald, “Über Beziehungen zwischen den Theorien der Parallelübertragung in Finslerschen Räumen,” Nederl. Akad. Weten. Proc, 49: 642–647 (1946);

    MathSciNet  MATH  Google Scholar 

  168. L. Berwald, “Über Beziehungen zwischen den Theorien der Parallelübertragung in Finslerschen Räumen,” Indagationes Math., 8:401–406 (1946).

    Google Scholar 

  169. L. Berwald, “Über Finslerschen und Cartansche Geometrie. IV. Projektiv-krümmung allgemeiner affiner Räume und Finslerscher Räume skalaler Krümmung,” Ann. Math., Ser. 2, 48: 755–781 (1949).

    Google Scholar 

  170. W. Bettingen, “Zum Satz von Gauss-Bonnet in der dreidimensionalen metrischen Differentialgeometrie,” Rend. Circolo Mat. Palermo, 9(3): 347–359 (1960).

    Google Scholar 

  171. W. Blaschke, “Integralgeometrie. XI. Zur Variationsrechnung,” Abhandl. Math. Sem. Univ. Hamburg, 11:359–366 (1936).

    Google Scholar 

  172. G. A. Bliss, “A generalization of the notion of angle,” Trans. Am. Math. Soc, 7:184–196 (1906).

    MathSciNet  MATH  Google Scholar 

  173. E. Bompiani, “Enti geometrici definiti da sistemi differenziali,” Atti Accad. Naz. Lincei. Rend. C1. Sci. Fis. Mat. Nat., 8(1): 187–194 (1946).

    Google Scholar 

  174. E. Bortolotti, “Geometry of a system of partial differential equations,” Tensor, 4:25–34(1941).

    MathSciNet  Google Scholar 

  175. F. Brickell, “On the existence of metric differential geometries based on the notion of area,” Proc. Cambridge Phil. Soc, 46:67–72 (1950).

    MathSciNet  MATH  Google Scholar 

  176. F. Brickell, “On areal spaces,” Tensor, 13:19–30 (1963).

    MathSciNet  MATH  Google Scholar 

  177. G. M. Brown, “Metric differential geometry,” Doctoral Dissertation, University of Toronto, 1965;

    Google Scholar 

  178. G. M. Brown, “Metric differential geometry,” Dissertation Abstr., B27(4):1211 (1966).

    Google Scholar 

  179. I. Bucur, “Asupra unei proprietati globale a linlilor geodezice ale unui spa-tiu,” Commun. Acad. RPR, 5(6): 965–968 (1955).

    MathSciNet  MATH  Google Scholar 

  180. H. Busemann, “On normal coordinates in Finsler spaces,” Math. Ann., 129(5): 417–423 (1955).

    MathSciNet  MATH  Google Scholar 

  181. H. Busemann, The Geometry of Geodesic, Academic Press, New York (1955).

    Google Scholar 

  182. E. Cartan, “Sur les variétés à connexion projective,” Bull. Soc. Math. France, 52:205–241 (1924).

    MathSciNet  MATH  Google Scholar 

  183. E. Cartan, “Les espaces de Finsler”. (Actual. Scient, et Industr., No. 79), Paris (1934).

    MATH  Google Scholar 

  184. E. Cartan, “Las espaces métriques fondés sur la notion d’aire,” Paris (1933) (Exposes de géometrie, 72).

    Google Scholar 

  185. S. Chern, “Sur la géometrie d’une équation différentielle du troisiéme ordre,” Compt. Rend. Acad. Sci., 204:1227–1229 (1937).

    Google Scholar 

  186. S. Chern, “On the Euclidean connections in a Finsler space,” Proc. Nat. Acad. Sci. USA, 29:33–37 (1943).

    MathSciNet  MATH  Google Scholar 

  187. S. Chern, “Local equivalence and Euclidean connection in Finsler spaces,” Sci. Rept. Nat. Tsing. Hua Univ., Ser. A, 5: 95–121 (1948).

    MathSciNet  Google Scholar 

  188. H. V. Craig, “On a generalized tangent vector,” Am. J. Math, 57:457–462 (1935).

    MathSciNet  Google Scholar 

  189. H. V. Craig, Vector and Tensor Analysis, McGraw-Hill, New York (1943).

    MATH  Google Scholar 

  190. E. T. Davies, “On the use of osculating spaces,” Tensor, 14: 86–98 (1963).

    MathSciNet  MATH  Google Scholar 

  191. E. T. Davies, “The geometry of a multiple integral,” J. London Math. Soc, 20:163–170 (1945).

    MathSciNet  MATH  Google Scholar 

  192. E. T. Davies, “Areal spaces,” Ann. Mat. Pura ed Appl., 55: 63–76 (1961).

    MATH  Google Scholar 

  193. R. Debever, “Sur une structure infinitésimale reguliére associée aux intégrales d’hypersurfaces du calcul de variations,” in: Convegno Internationale di Geometria Differenziale, Italy, 1953, Ed, Gremonese, Rome (1954), pp. 214–221.

    Google Scholar 

  194. R. Debever, “Sur une classe d’espaces,” Thesis, Brussells (1947).

    Google Scholar 

  195. A. Deike, “Über die Darstellung von Finsler-Räumen durch nichtholonome Mannigfaltigkeiten in Riemannschen Räumen,” Arch. Math., 4(3): 234–238 (1953).

    MathSciNet  Google Scholar 

  196. A. Deike, “Finsler spaces as nonholonomic subspaces of Riemannian spaces,” J. London Math. Soc, 30(1): 53–58 (1955).

    MathSciNet  Google Scholar 

  197. A. Deike, “Über die Finsler-Räume mit A i = 0,” Arch. Math., 4: 45–51 (1953). (1953).

    MathSciNet  Google Scholar 

  198. M. Dhawan, “Curvature properties of a subspace embedded in a Finsler space,” Ganita, 16(1): 25–36 (1965).

    MathSciNet  MATH  Google Scholar 

  199. M. Dhawan and N. Prakash, “Generalizations of Gauss — Codazzi equations in a subspace embedded in a Finsler manifold,” Tensor, 15(2): 159–167 (1964).

    MathSciNet  MATH  Google Scholar 

  200. J. Douglas, “The general geometry of paths,” Ann. Math., 29:143–168 (1928).

    MATH  Google Scholar 

  201. J. Douglas, “Systems of K-dimensional manifolds in an n-dimensional space,” Math. Ann., 105:707–733 (1931).

    MathSciNet  Google Scholar 

  202. V. Dumitras, “Sur le groupe de stabilité d’un espace Hn,” Bull. Math. Soc. Sci. Math, et Phys. RPR, 3(1): 17–20 (1959).

    MathSciNet  Google Scholar 

  203. L. P. Eisenhart, “Finsler spaces derived from Riemann spaces by contact transformations,” Ann. Math., Ser. 2, 49:227–254 (1948).

    MathSciNet  Google Scholar 

  204. H.A. Eliopoulos, “Methods of generalised metric geometry with applications to mathematical physics,” Thesis, Toronto (1956), 112 pp.

    Google Scholar 

  205. H. A. Eliopoulos, “Sur la définition de la courbure totale d’une hypersurface plongée dans un espace de Finsler localement Minkowskien,” Bull. Cl. Sci. Acad. Roy. Belg., 45(3): 205–214 (1959).

    MathSciNet  MATH  Google Scholar 

  206. H. A. Eliopoulos, “Multi-particle theory derived from the geometry of a locally Minkowskian Finsler space,” Bull. C1. Sci. Acad. Roy. Belg., 52(1): 69–75(1966).

    MathSciNet  MATH  Google Scholar 

  207. P. Finsler, “Über Kurven und Flächen in allgemeinen Räumen,” Dissertation, Göttingen (1918).

    Google Scholar 

  208. P. Finsler, Über Kurven und Flächen in allgemeinen Räumen, Basel (1951).

    MATH  Google Scholar 

  209. P. Finsler, “Über die Krümmungen der Kurven und Flächen,” in: Reale Accad. Ital., Fondazione Alessandro Volta, IX Convegno Volta, Rome (1940).

    Google Scholar 

  210. P. Finsler, “Über eine Verallgemeinerung der Satzes von Meusnier,” Viertel. Naturforsch. Ges. Zürich, Supplement 85, pp. 155–164 (1940).

    MathSciNet  Google Scholar 

  211. J. G. Freeman, “First and second variations of the length integral in a generalized metric space,” Quart. J. Math., Oxford, Ser. 15, pp. 70–83 (1944).

    MathSciNet  MATH  Google Scholar 

  212. J. G. Freeman, “Finsler-Riemann systems,” Quart. J. Math., 7(26): 100–109 (1956).

    MathSciNet  MATH  Google Scholar 

  213. J. G. Freeman, “Complete Finsler-Riemann systems,” Quart. J. Math., 8(31): 161–171 (1957).

    MathSciNet  MATH  Google Scholar 

  214. M. Fujinaka, “On Finsler spaces and dynamics with special reference to the equations of hunting,” in: Proc. 3rd Jap. Nat. Congress Appl. Mechanics, Tokyo (1954), pp. 433–436.

    Google Scholar 

  215. P. Funk, “Eine Kennzeichnung der zwei-dimensionalen elliptischen Geometrie,” Sitzber. Österr. Akad. Wiss. Math.-Naturwiss. K1., Abt. 2, 172(9–10): 251–269(1963).

    MathSciNet  Google Scholar 

  216. O. Galvani, “Sur la réalisation des espaces de Finsler,” Compt. Rend. Acad. Sci., Paris, 222:1067–1069 (1946).

    MathSciNet  MATH  Google Scholar 

  217. O. Galvani, “Les connexions finsleriennes de congruences de droites,” Compt. Rend. Acad. Sci. Paris, 222:1200–1202 (1946).

    MathSciNet  MATH  Google Scholar 

  218. O. Galvani, “Sur l’immersion du plan de Finsler dans certains espaces de Riemann a trois dimensions,” Compt. Rend. Acad. Sci., 223:1088–1090 (1946).

    MathSciNet  MATH  Google Scholar 

  219. O. Galvani, “La réalization des connexions euclidiennes d’éléments linéaires et des espaces de Finsler,” Ann. Inst. Fourier, Grenoble, 2:123–146 (1950).

    MathSciNet  MATH  Google Scholar 

  220. O. Galvani, “La réalisation des espaces de Finsler,” Compt. Rend. Congrès. Soc. Savantes Paris et des Departements, Grenoble (1952), pp. 57–60.

    Google Scholar 

  221. O. Galvani, “Réalisations euclidiennes des plans de Finsler,” Ann. Inst. Fourier, 5:421–454 [1953–1954 (1955)].

    MathSciNet  Google Scholar 

  222. M. Gama, “On areal spaces of submetric class,” Tensor, 16(3): 262–268 (1965).

    MathSciNet  Google Scholar 

  223. M. Gama, “On areal spaces of the submetric class. II,” Tensor, 16(3): 291–293 (1965).

    MathSciNet  Google Scholar 

  224. M. Gama, “On areal spaces of the submetric class. III,” Tensor, 17(1): 79–85 (1966).

    MathSciNet  Google Scholar 

  225. M. Gama, “On areal spaces of the submetric class. IV,” Tensor, 18(1): 49–53 (1967).

    MathSciNet  MATH  Google Scholar 

  226. M. Gama, “Theory of subspaces in areal spaces of the submetric class,” Tensor, 18(2): 168–180 (1967).

    MathSciNet  MATH  Google Scholar 

  227. St. Gołab, “Einige Bemerkungen über Winkelmetrik in Finslerschen Räumen,” Verhandl. Intern. Math. Kongresses Zürich, 11:178–179 (1932).

    Google Scholar 

  228. St. Goiab, “Sur la representations conforme de l’espace euclidien,” Compt. Rend. Acad. Sci. Paris, 196:25–27 (1933).

    Google Scholar 

  229. St. Gołab, “Sur la representation conforme de deux espaces de Finsler,” Compt. Rend. Acad. Sci., Paris, 196: 986–988 (1933).

    Google Scholar 

  230. St. Gobab, “Sur la mesure des aires dans les espaces de Finsler,” Compt. Rend. Acad. Sci., Paris, 200:197–199 (1935).

    Google Scholar 

  231. St. Goiab, “On Finsler’s measurement of angle,” Ann. Soc. Polon. Math., 24:78–84(1954).

    Google Scholar 

  232. H. H. Goldstine, “The calculus of variations in abstract spaces,” Duke Math. J., 9:811–822(1942).

    MathSciNet  Google Scholar 

  233. N. Grossman, “On real projective spaces as Finsler manifolds,” Proc. Am. Math. Soc, 18(2): 325–326 (1967).

    MathSciNet  MATH  Google Scholar 

  234. A. Haimovici, “Geometria unei ecutii Monge de tip particular,” Studii Si Cercetäri Stint., 5(1–2): 17–27 (1954).

    MathSciNet  MATH  Google Scholar 

  235. M. Haimovici, “Formules fondamentales dans la theorie des hypersurfaces d’un espace de Finsler,” Compt. Rend. Acad. Sci., Paris, 198:426–427 (1934).

    Google Scholar 

  236. M. Haimovici, “Sur les espaces généraux qui se correspondent point par point avec conservation du parallélisme de Cartan,” Compt. Rend. Acad. Sci., Paris, 198:1105–1108 (1934).

    Google Scholar 

  237. M. Haimovici, “Sur quelques types de metriques de Finsler,” Compt. Rend. Acad. Sci., Paris, 199:1091–1093 (1934).

    Google Scholar 

  238. M. Haimovici, “Sur les espaces de Finsler à connexion affine,” Compt. Rend. Acad. Sci., Paris, 204:837–839 (1937).

    Google Scholar 

  239. M. Haimovici, “La parallélisme dans les espaces de Finsler et la differentiation invariante de M. Levi-Civita,” Ann. Sci. Univ. Jassy, 24: 214–218 (1938).

    Google Scholar 

  240. M. Haimovici, “Sulle superficie totalemente geodetiche negli spazi di Finsler,” Rend. Lincei, 27:633–641 (1938).

    Google Scholar 

  241. M. Haimovici, “Variétés totalement extremales et variétés totalement géo-désiques dans les espaces de Finsler,” Ann. Sci. Univ. Jassy, 25: 559–644 (1939).

    Google Scholar 

  242. M. Hashiguchi, “On parallel displacements in Finsler spaces,” J. Math. Soc. Japan, 10(4): 365–379 (1958).

    MathSciNet  MATH  Google Scholar 

  243. H. Hashimoto, “On the geometry of a system of partial differential equations of third order,” Tensor, 4: 55–59 (1941).

    MathSciNet  Google Scholar 

  244. H. Hashimoto, “On the geometry of a system of partial differential equations of third order,” J. Fac. Sci. Hokkaido Univ., Ser. Math., 8(14): 163–172 (1940).

    Google Scholar 

  245. E. Heil, “A relation between Finslerian and Hermitian metrics,” Tensor, 16(1): 1–3 (1965).

    MathSciNet  MATH  Google Scholar 

  246. E. Heil, “Eine Charakterisierung lokal-Minkowskischer Räume,” Math. Ann., 167(1): 64–70 (1966).

    MathSciNet  MATH  Google Scholar 

  247. H. Hiramatsu, “On affine collineations in a space of hyperplanes,” Kumamoto J. Sci., 1:1–7 (1952).

    Google Scholar 

  248. H. Hiramatsu, “On projective collineations in a space of hyperplanes,” Tensor, New Series, 2:1–14 (1952).

    Google Scholar 

  249. H. Hiramatsu, “On some properties of groups of homothetic transformations in Riemannian and Finslerian spaces,” Tensor, 4: 28–29 (1954).

    MathSciNet  Google Scholar 

  250. H. Hiramatsu, “Groups of homothetic transformations in a Finsler space,” Tensor, 3(3): 131–143 (1954).

    MathSciNet  Google Scholar 

  251. S. Hokari, “Winkeltreue Transformationen und Bewegungen im Finslerschen Räume,” J. Fac. Sci. Hokkaido Univ., 5:1–8 (1936).

    Google Scholar 

  252. S. Hokari, “Geometry in an n-dimensional space based on the idea of K-dimensional volume,” Tensor, 4: 72–77 (1941).

    MathSciNet  Google Scholar 

  253. S. Hokari, “On a geometrical treatment of a system of higher partial differential equations,” Tensor, 5:89–103 (1942).

    MathSciNet  Google Scholar 

  254. E. Hölder, “Über die auf Extremalintegrale gegründeten metrischen Räume,” Schr. Forschungsinst. Math., 1:178–193 (1957).

    MathSciNet  Google Scholar 

  255. H. Hombu, “Konforme Invarianten im Finslerschen Raum,” J. Fac. Sci. Hokkaido Univ., Ser. I, Math., 2:157–168 (1934).

    Google Scholar 

  256. H. Hombu, “Konforme Invarianten im Finslerschen Raum,” J. Fac. Sci. Hokkaido Univ., Ser. I, Math., 4: 51–66 (1935).

    Google Scholar 

  257. H. Hombu, “Die Krümmungstheorie im Finslerschen Raum,” J. Fac. Sci. Hokkaido Univ., Ser. I., Math., 5:67–94 (1936).

    Google Scholar 

  258. J. I. Horváth, “Un model geometric pentru teoria unitaria a campurilor fizi-ce. Studdii si cercetǎri fiz.,” Acad. RPR, 4(1–2): 109–111 (1953).

    Google Scholar 

  259. J. I. Horvath, “Contribution to Stephenson-Kilmister’s unified theory of gravitation and electromagnetism,” Nuovo Cimento, 4(3): 571–576 (1956).

    MATH  Google Scholar 

  260. J. I. Horváth, “New geometrical methods of the theory of physical fields,” Nuovo Cimento, 9, Suppl., No. 2:444–496 (1958).

    MATH  Google Scholar 

  261. J.I. Horváth and A. Moor, “Entwicklung einer Feldtheorie begründet auf einen allgemeinen metrischen Linienelementraum. I, II,” Proc. Koninkl. Ned. Akad. Wetenschap., A58(4): 421–430;A58(5): 581–587 (1955).

    Google Scholar 

  262. J. I. Horváth, “A italanos metricus vonalelementérre alapozott térelmélet,” Magy. Tud. Akad. Mat. Fiz. Tud. Oszt. Közl., 6(1): 53–72 (1956).

    MATH  Google Scholar 

  263. T. Hosokawa, “On the various linear displacements in the Berwald-Finsler’s manifold,” Sci. Rept. Tokyo, 19:37–51 (1930).

    MATH  Google Scholar 

  264. T. Hosokawa, “Finslerian wave geometry and Milne’s world structure,” J. Sci. Hiroshima Univ., A8: 249–270 (1938).

    Google Scholar 

  265. Hou-Sung Hu, “A new geometry of a space of K-spreads,” Sci. Rec, 3(3): 107–111(1959).

    MATH  Google Scholar 

  266. Hou-Sung Hu, “A Finslerian product of two Riemannian spaces,” Sci. Rec, 3(10): 446–448 (1959).

    MATH  Google Scholar 

  267. S. Ide, “On the connections in higher order spaces,” Tensor, 4(3): 135–140 (1955).

    MathSciNet  MATH  Google Scholar 

  268. S. Ide, “On the theory of curves in an n-dimensional space with the metrics s = ∫ {A i (x,x’)x” i + B(x,x’)} 1/p dt,” Tensor, 9:25–29(1949).

    MathSciNet  Google Scholar 

  269. S. Ide, “On the geometrical meanings of Wirtinger’s connections based on Kawaguchi’s,” Tensor, 14:216–218 (1963).

    MathSciNet  MATH  Google Scholar 

  270. T. Igarashi, “On Lie derivaties in areal spaces,” Tensor, 18(2): 205–211 (1967).

    MathSciNet  MATH  Google Scholar 

  271. R. S. Ingarden, “Über die Einbettung eines Finslerschen Raumes in einen Minkowskischen Raum,” Bull. Acad. Polon. Sci., C1. 3, 2(7): 305–308 (1954).

    MathSciNet  MATH  Google Scholar 

  272. R. S. Ingarden, “Über die Einbettung eines Finslerschen Raumes in einen Minkowskischen Raum,” Bull. Acad. Polon. Sci., C1. 3, 2(7): 309–311 (1954).

    Google Scholar 

  273. S. Ishihara and T. Fukami, “Groups of projective transformations in a space of K-spreads,” Japan J. Math., 26:79–93 (1956).

    MathSciNet  Google Scholar 

  274. C. I. Ispas, “Identités de type Ricci dans l’espace de Finsler,” Comun. Acad. RPR, 2:13–18(1952).

    Google Scholar 

  275. H. Iwamoto, “On the conformai theory of metric geometry of higher order,” Tensor, 7:50–57 (1944).

    MathSciNet  Google Scholar 

  276. H. Iwamoto, “La géométrie des espaces métriques fondés sur la notion d’aire. I,” Proc. Japan. Acad., 21:119–123 (1945).

    MathSciNet  Google Scholar 

  277. H. Iwamoto, “La géométrie des espaces métriques fondés sur la notion d’aire. II,” Proc. Japan. Acad., 21:223–226 (1945).

    MathSciNet  Google Scholar 

  278. H. Iwamoto, “On geometries associated with multiple integrals,” Jap. J. Math., 1(1): 74–91 (1948).

    MathSciNet  MATH  Google Scholar 

  279. H. Iwamoto, “Über eine geometrische Theorie der mehrfachen Integrale,” Jap. J. Math., 19:479–512 (1948).

    MathSciNet  Google Scholar 

  280. H. Iwamoto, “On the geometry in a space based on the notion of area. I, II,” Tensor, 9: 7–12 (1949); 9:13–17 (1949).

    MathSciNet  Google Scholar 

  281. C. Kano, “Conformai geometry in an n-dimensional space with the arc length s = ∫ {(A i (x, x’)x ”i +B(x, x ’ )) 1/p dt,” Tensor, 5(3): 187–196 (1956).

    MathSciNet  MATH  Google Scholar 

  282. C. Kano, “Conformai geometry in an n-dimensional space with the arc length ∫ {(A i (x, x’)x ”i +B(x, x ’ )) 1/p dt, II,” Tensor, 10(3): 210–217 (1960).

    Google Scholar 

  283. S. Kashiwabara, “On Euclidean connections in a Finsler manifold,” Toho-ku Math. J., 10(1): 69–80 (1958).

    MathSciNet  MATH  Google Scholar 

  284. Y. Katsurada, “On the theory of curves in a higher order space with some special metrics,” Tensor, 7: 58–64 (1944).

    MathSciNet  Google Scholar 

  285. R. N. Kaul, “Curvatures in Finsler space,” Bull. Calcutta Math. Soc., 50(4): 189–192 (1958).

    MathSciNet  MATH  Google Scholar 

  286. A. Kawaguchi, “Theory of connections in the generalized Finsler manifold,” Proc. Imp. Acad. Tokyo, 7(6): 211–214 (1931).

    MathSciNet  Google Scholar 

  287. A. Kawaguchi, “Theory of connections in generalized Finsler manifold. II,” Proc. Imp. Acad. Tokyo, 8(8): 340–343 (1932).

    MathSciNet  Google Scholar 

  288. A. Kawaguchi, “Theory of connections in the generalized Finsler manifold,” Proc. Imp. Acad. Tokyo, 9(6):347–350 (1933).

    MathSciNet  Google Scholar 

  289. A. Kawaguchi, “Some intrinsic derivations in a generalized space,” Proc. Imp. Acad. Tokyo, 12(6): 149–152 (1936).

    MathSciNet  Google Scholar 

  290. A. Kawaguchi, “Certain identities in a generalized space,” Proc. Imp. Acad. Tokyo, 12(6): 152–155 (1936).

    MathSciNet  Google Scholar 

  291. A. Kawaguchi, Die Geometrie des Integrals ∫ {A i x “i + B} 1/p dt.,” Proc. Imp. Acad. Tokyo, 12:205–208 (1936).

    MathSciNet  Google Scholar 

  292. A. Kawaguchi, “Ein metrischer Raum, der eine Verallgemeinerung des Finslerschen Raumes ist,” Monatsh. Math. Phys., 43:289–297 (1936).

    MathSciNet  Google Scholar 

  293. : A. Kawaguchi, “Theorie des Raumes mit dem Zusammenhang, der von abhänggig ist,” Monatsh. Math. Phys., 44:131–152 (1936).

    MathSciNet  Google Scholar 

  294. A. Kawaguchi, “Theory of connections in a Kawaguchi space of order two,” Proc. Imp. Acad. Tokyo, 13:183–186 (1937).

    MathSciNet  Google Scholar 

  295. A. Kawaguchi, “Theory of connections in a Kawaguchi space of higher order,” Proc. Imp. Acad. Tokyo, 13:237–240 (1937).

    MathSciNet  Google Scholar 

  296. A. Kawaguchi, “Views on higher order geometry of connections. I, II, III,” Tensor, 1:13–18 (1938);

    Google Scholar 

  297. A. Kawaguchi, “Views on higher order geometry of connections. I, II, III,” 2:39–45 (1939);

    Google Scholar 

  298. A. Kawaguchi, “Views on higher order geometry of connections. I, II, III,” 3: 68–70 (1940).

    Google Scholar 

  299. A. Kawaguchi, “Die Differentialgeometrie höherer Ordnung. I. Erweiterte Koordinatentransformationen und Extensoren,” J. Fac. Sci. Hokkaido Univ., Ser. I., 9:1–152 (1940).

    MathSciNet  Google Scholar 

  300. A. Kawaguchi, “Die Differentialgeometrie höherer Ordnung. II. Über die n-dimensionalen Flächenelement abhängigem Zusammenhang,” J. Fac. Sci. Hokkaido Imp. Univ., Ser. I, 9:153–188 (1940).

    MathSciNet  Google Scholar 

  301. A. Kawaguchi, “Die Differentialgeometrie höherer Ordnung. III. Erweiterte Parametertransformationen und P-Tensoren,” J. Fac. Sci. Hokkaido Univ., 10:77–156 (1941).

    MathSciNet  MATH  Google Scholar 

  302. A. Kawaguchi, “Views on higher order geometry of connections. IV,” Tensor, 4:66–68(1941).

    MathSciNet  Google Scholar 

  303. A. Kawaguchi, “Determination of the fundamental tensor in a five-dimensional space based on two-dimensional area,” Tensor, 6:49–61 (1943).

    MathSciNet  Google Scholar 

  304. A. Kawaguchi, “On various tensors appearing in the higher order geometry of connection,” Tensor, 6:1–26 (1943).

    MathSciNet  Google Scholar 

  305. A. Kawaguchi, “On certain metric space of higher order,” Tensor, 7: 73–77 (1944).

    MathSciNet  Google Scholar 

  306. A. Kawaguchi, “On areal spaces. I,” Tensor, 1:14–45 (1950).

    MathSciNet  Google Scholar 

  307. A. Kawaguchi, “On areal spaces. II,” Tensor, 1: 67–88 (1951).

    MathSciNet  MATH  Google Scholar 

  308. A. Kawaguchi, “On areal spaces. III,” Tensor, 1: 89–101 (1951).

    MathSciNet  MATH  Google Scholar 

  309. A. Kawaguchi, “Generalizzationi del calcolo tenzoriale e delle sue appli-cazioni,” Atti Accad. Lincei. Rend. C1. Sci., Fis., Mat. e Natur., 15(5): 255–261 (1953).

    MathSciNet  MATH  Google Scholar 

  310. A. Kawaguchi, “Theory of areal spaces,” Rend. Mat. e Applic., 12(3–4):373–386 (1953).

    MathSciNet  Google Scholar 

  311. A. Kawaguchi, “A remark to the theory of areal spaces,” Nieuw Arc. Wiskunde, 2(2–3): 115–117 (1954).

    MathSciNet  MATH  Google Scholar 

  312. A. Kawaguchi, “On the theory of nonlinear connections. II. Theory of nonlinear connections in a Finsler space,” Tensor, 6(3): 165–199 (1956).

    MathSciNet  MATH  Google Scholar 

  313. A. Kawaguchi, “Die Differentialgeometrie höherer Ordnung. IV. Erweiterung der verallgemeinerten Rheonomtransformation von Flächenelementen höherer Ordnung und Rk-Extensoren,” Publ. Math., 7(1–4): 256–276 (1960).

    MathSciNet  MATH  Google Scholar 

  314. A. Kawaguchi, “On functional form of integral invariants,” Math. Notae, 18(1): 109–116 (1962).

    MathSciNet  Google Scholar 

  315. A. Kawaguchi and H. Hombu, “Die Geometrie des Systems der partiellen Differentialgleichungen,” J. Fac. Sci. Hokkaido Univ., Ser. I, 6(1): 21–62 (1937).

    Google Scholar 

  316. A. Kawaguchi and K. Tandai, “On areal spaces. IV,” Tensor, 2:47–58 (1952).

    MathSciNet  MATH  Google Scholar 

  317. M. Kawaguchi, “An introduction to the theory of higher order spaces. I. The theory of Kawaguchi spaces,” in: RAAG Mem. Unifying Study Basic Prob. Engng. and Phys. Sci. Means Geom., Vol. 3, Tokyo, Gakujutsu Bunken Fukyukai (1962), pp. 718–734.

    Google Scholar 

  318. M. Kawaguchi, “Une observation sur le calcul des calottes,” Tensor, 14:182–190 (1963).

    MathSciNet  Google Scholar 

  319. S. Kawaguchi, “On some properties of projective curvature tensor in a special Kawaguchi space,” Tensor, 13:83–88 (1963).

    MathSciNet  MATH  Google Scholar 

  320. S. Kawaguchi, “On a special Kawaguchi space of recurrent curvature,” Tensor, 15(2): 145–158 (1964).

    MathSciNet  MATH  Google Scholar 

  321. S. Kawaguchi and T. Nobuhara, “On extremal curves in a special Kawaguchi space,” Tensor, 5(3): 197–200 (1956).

    MathSciNet  MATH  Google Scholar 

  322. M. A. McKiernan, “Sufficiency of parameter invariance conditions in areal and higher order Kawaguchi spaces,” Publ. Math., 13(1–4): 77–85 (1966).

    MathSciNet  MATH  Google Scholar 

  323. Shigetaka Kikuchi, “Theory of Minkowski space and of nonlinear connections in a Finsler space,” Tensor, 12(1): 47–60 (1962).

    MathSciNet  MATH  Google Scholar 

  324. Shigetaka Kikuchi, “Some remarks on areal spaces of the submetric class,” Tensor, 17(1): 44–48 (1966).

    MathSciNet  Google Scholar 

  325. J. Klein, “Sur les trajectoires d’un système dynamique dans un espace finslérien ou variationnel généralisé,” Compt. Rend. Acad. Sci., 238(22): 2144–2146 (1954).

    MATH  Google Scholar 

  326. M. S. Knebelmann, “Motions and collineations in general space,” Proc. Nat. Acad. Sci. USA, 13:607–611 (1927).

    Google Scholar 

  327. M. S. Knebelmann, “Collineations and motions in generalized spaces,” Am. J. Math., 51:527–564(1929).

    Google Scholar 

  328. S. Kobayashi, “Groupe de transformations qui laissent invariante une connexion infinitésimale,” Compt. Rend. Acad. Sci. Paris, 238:644–645 (1954).

    MATH  Google Scholar 

  329. S. Kobayashi, “Le groupe des transformationes qui laissent invariant le parallélisme,” Coll. de Topologie, Strasbourg (1954).

    Google Scholar 

  330. K. Kondo, “On the theoretical investigation based on abstract geometry of dynamical systems appearing in engineering,” in: Proc. 3rd. Jap. Nat. Congress Appl. Mechanics, Tokyo (1954), pp. 425–432.

    Google Scholar 

  331. D. D. Kosambi, “Parallelism and path-space,” Math. Z., 37: 608–618 (1933).

    MathSciNet  Google Scholar 

  332. D. D. Kosambi, “Lie rings in path space,” Proc. Nat. Acad. Sci. USA, 35:389-a94 (1949).

    MathSciNet  MATH  Google Scholar 

  333. R. Kreter, “Zusammenhänge in Finslerschen Räumen,” Wiss. Z. Humboldt Univ., Berlin, Math.-Naturwiss. Reihe, 6(4): 353–365 (1956–1957).

    MathSciNet  Google Scholar 

  334. Chao-Hao Ku, “On the descriptive geometry of a space of K-spreads,” Acad. Sinica Sci. Record, 3: 53–59 (1950).

    MATH  Google Scholar 

  335. Chao-Hao Ku, “New treatment of geometry in a space of K-spreads,” Acad. Sinica Sci. Record, 3:41–51 (1950).

    MATH  Google Scholar 

  336. Chao-Hao Ku, “On Finsler spaces admitting a group of motions of the greatest order,” Sci. Rec., 1(4):215–218 (1957).

    MATH  Google Scholar 

  337. M. Kurita, “On the dilatation in Finsler spaces,” Osaka Math. J., 15(1): 87–98 (1963).

    MathSciNet  MATH  Google Scholar 

  338. M. Kurita, “Theory of Finsler spaces based on the contact structure,” J. Math. Soc. Japan, 18(2): 119–134 (1966).

    MathSciNet  MATH  Google Scholar 

  339. G. Landsberg, “Über die Totalkrümmung,” Jahresberichte Deut. Math.-Ver., 16:36–46 (1907).

    MATH  Google Scholar 

  340. G. Landsberg, “Krümmungstheorie und Variationsrechnung,” Jahresberichte Deut. Math.-Ver., 16:547–551 (1907).

    MATH  Google Scholar 

  341. G. Landsberg, “Über die Krümmung in der Variationsrechnung,” Math. Ann., 65:313–349(1908).

    MathSciNet  MATH  Google Scholar 

  342. D. Laugwitz, “Zur geometrischen Begründungen der Parallelverschiebung in Finslerschen Räumen,” Arch. Math., 6(6): 448–453 (1955).

    MathSciNet  MATH  Google Scholar 

  343. D. Laugwitz, “Die Vektorübertragungen in der Finslerschen Geometrie und der Wegegeometrie,” Proc. Koninkl. Ned. Akad. Wetenschap., A59(1):21–28 (1956);

    Google Scholar 

  344. D. Laugwitz, “Die Vektorübertragungen in der Finslerschen Geometrie und der Wegegeometrie,” Indagationes Math., 18(1): 21–28 (1956).

    MathSciNet  Google Scholar 

  345. D. Laugwitz, “Zur projectiven und konformen Geometrie der Finsler Räume,” Arch. Math., 7(1): 74–77 (1956).

    MathSciNet  MATH  Google Scholar 

  346. D. Laugwitz, “Grundlagen für die Geometrie der unendlichdimensionalen Finsler-Räume,” Ann. Mat. Pura ed Appl., 41:21–41 (1956).

    MathSciNet  MATH  Google Scholar 

  347. D. Laugwitz, “Zur Differentialgeometrie der Hyperflachen in Vektorräumen und zur affingeometrischen Deutung der Theorie der Finsler-Räume,” Math. Z., 67(1): 63–74 (1957).

    MathSciNet  MATH  Google Scholar 

  348. D. Laugwitz, “Eine Beziehung zwischen affiner und Minkowskischer Differentialgeometrie,” Publ. Math., 5(1–2): 72–76 (1957).

    MathSciNet  Google Scholar 

  349. D. Lehmann, “Théorie de Morse en géométrie finslérienne,” Cahiers Semin. Topol. et Géom. Différent. Ch. Ehresmann, Fac. Sci., Paris, Vol. 6 (1964).

    Google Scholar 

  350. A. Lichnerowicz, “Les espaces à connexion semi-symétrique et la mécanique,” Compt. Rend. Acad. Sci. Paris, 212:328–331 (1941).

    MathSciNet  Google Scholar 

  351. A. Lichnerowicz, “Sur une généralisation des espaces de Finsler,” Compt. Rend. Acad. Sci., Paris, 214:599–601 (1942).

    MathSciNet  Google Scholar 

  352. A. Lichnerowicz, “Sur une extension de la formule d’Allendorerfer-Weil à certaines variétés finslériennes,” Compt. Rend. Acad. Sci., Paris, 223:12–14 (1946).

    MathSciNet  MATH  Google Scholar 

  353. A. Lichnerowicz and Y. Thiry, “Problémes de calcul des variations liés à la dynamique classique et à la théory unitaire du champ,” Compt. Rend. Acad. Sci. Paris, 224:529–531 (1947).

    MathSciNet  MATH  Google Scholar 

  354. H. Lippmann, “Zur Winkeltheorie in zweidimensionalen Minkowski- und Finsler-Räumen,” Proc. Koninkl. Ned. Akad. Wetenschap., A60(2): 162–170 (1957);

    MathSciNet  Google Scholar 

  355. H. Lippmann, “Zur Winkeltheorie in zweidimensionalen Minkowski- und Finsler-Räumen,” Indagationes Math., 19(2): 162–170 (1957).

    MathSciNet  Google Scholar 

  356. H. Lippmann, “Metrische Eigenschaften verschiedener Winkelmasse in Minkowski und Finsler-Räumen. II,” Proc. Koninkl. Akad. Wetenschap., A61(2): 223–230 (1958);

    Google Scholar 

  357. H. Lippmann, “Metrische Eigenschaften verschiedener Winkelmasse in Minkowski und Finsler-Räumen. II,” Indagationes Math., 20(2): 223–230 (1958).

    Google Scholar 

  358. H. Lippmann, “Metrische Eigenschaften verschiedener Winkelmasse in Minkowski- und Finsler-Räumen. II,” Proc. Koninkl. Akad. Wetenschap., A6(2): 231–238 (1958);

    Google Scholar 

  359. H. Lippmann, “Metrische Eigenschaften verschiedener Winkelmasse in Minkowski- und Finsler-Räumen. II,” Indagationes Math., 20(2): 231–238 (1958).

    Google Scholar 

  360. T. Maebashi, “A weakly osculating Riemann space of the Finsler space and its application to a theory of subspaces in the Finsler space,” Tensor, 9(1): 62–72 (1959).

    MathSciNet  MATH  Google Scholar 

  361. M. Matsumoto, “A global fundation of Finsler geometry,” Mem. Coll. Sci., Univ. Kyoto, A33(l): 171–208 (1960).

    Google Scholar 

  362. M. Matsumoto, “Affine transformations of Finsler spaces,” J. Math. Kyoto Univ., 3(1): 1–35 (1963).

    MathSciNet  MATH  Google Scholar 

  363. M. Matsumoto, “Linear transformations of Finsler connections,” J. Math. Kyoto Univ., 3(2): 145–167 (1964).

    MathSciNet  MATH  Google Scholar 

  364. M. Matsumoto, “Paths in a Finsler space,” J. Math. Kyoto Univ., 3(3): 305–318 (1964).

    MathSciNet  MATH  Google Scholar 

  365. M. Matsumoto, “On R. Sulanke’s method deriving H. Rund’s connection in a Finsler space,” J. Math. Kyoto Univ., 4(2): 355–368 (1965).

    MathSciNet  MATH  Google Scholar 

  366. M. Matsumoto, “A Finsler connection with many torsions,” Tensor, 17(3): 217–226 (1966).

    MathSciNet  MATH  Google Scholar 

  367. K. Maurin, “Eingliedrige Gruppen der homogenen kanonischen Transformationen und Finslersche Räume,” Ann. Polon. Math., 2(1): 97–102 (1955).

    MathSciNet  MATH  Google Scholar 

  368. T. Michihiro, “Theory of curves in a two-dimensional space with arc length s = ∫(A i x ”i + B) 1/p dt,” Tensor, 4:63–66 (1941).

    MathSciNet  Google Scholar 

  369. M. Mikami, “Projective theory of a system of paths of higher order,” Tensor, 6:86–94(1943).

    MathSciNet  Google Scholar 

  370. M. Mikami, “Geometry of the integral s = ∫(A i x (m)i + B) 1/p dt,” Jap. J. Math., 18:663–673 (1943).

    MathSciNet  MATH  Google Scholar 

  371. R. Mirodan, “Geometrizarea ecuatiilor cu derivate partiale linaire si omogene,” An. Univ. “C. I. Parhon,” Ser. Stint. Natur., No. 14, pp. 35–39 (1957).

    Google Scholar 

  372. R. B. Misra, “The projective transformation in a Finsler space,” Ann. Soc. Sci. Bruxelles, Ser. 1, 80(3): 227–239 (1966).

    MATH  Google Scholar 

  373. R. B. Misra, “Projective tensors in a conformai Finsler space,” Bull. C1. Sci. Acad. Roy. Belg., 52(10): 1275–1279 (1966).

    MATH  Google Scholar 

  374. R. B. Misra, “The commutation formulae in a Finsler space. I,” Ann. Mat. Pura ed Appl., 75:363–370 (1967).

    Google Scholar 

  375. R. B. Misra, “The commutation formulae in a Finsler space. II,” Ann. Mat. Pura ed Appl., 75:371–383 (1967).

    Google Scholar 

  376. R. B. Misra, “The Bianchi identities satisfied by curvature tensors in a con-formal Finsler space,” Tensor, 18(2): 187–190 (1967).

    MathSciNet  MATH  Google Scholar 

  377. R. S. Mishra and R. S. Sinha, “Relative Frenet formulae for curves in a sub-space and a hypersurface of a Finsler space,” Tensor, 16(2): 114–132 (1956).

    MathSciNet  Google Scholar 

  378. R. S. Mishra and R. S. Sinha, “Union and hyperasymptotic curves of a Finsler subspace and hypersurface,” Rend. Circolo Mat. Palermo, 14(1): 119–128 (1965).

    MathSciNet  MATH  Google Scholar 

  379. R. S. Mishra and R. S. Sinha, “Union curvature of a curve in a Finsler space,” Tensor, 16(2): 160–168 (1965).

    MathSciNet  MATH  Google Scholar 

  380. R. S. Mishra and U. P. Singh, “On the union curvature of a curve of a Finsler space,” Tensor, 17(2): 205–211 (1966).

    MathSciNet  Google Scholar 

  381. F. Moalla, “Espaces de Finsler complets,” Compt. Rend. Acad. Sci., 258(8):2251–2254 (1964).

    MathSciNet  MATH  Google Scholar 

  382. F. Moalla, “Espaces de Finsler complets a courbure de Ricci positive,” Compt. Rend. Acad. Sci., 258(10): 2734–2737 (1964).

    MathSciNet  Google Scholar 

  383. F. Moalla, “Espaces de Finsler sans points conjugués,” Compt. Rend. Acad. Sci., 260(25): 6510–6512 (1965).

    MathSciNet  MATH  Google Scholar 

  384. A. Moor, “Finslersche Räume mit algebraischen Grundfunktionen,” Publ. Math., 2(3–4): 178–180 (1952).

    MathSciNet  Google Scholar 

  385. A. Moor, “Ergänzung zu meiner Arbeit: ‘Über die Dualität von Finslerschen und Cartanschen Räumen’,” Acta Math., 91(3–4): 187–188 (1954).

    MathSciNet  MATH  Google Scholar 

  386. A. Moor, “Die oskulierenden Riemannschen Räume regulärer Cartanscher Räume,” Acta Math. Acad. Sci. Hung., 5(1–2): 59–72 (1954).

    MathSciNet  MATH  Google Scholar 

  387. A. Moor, “Allgemeine metrische Räume von skalarer Krümmung,” Publ. Math. 4(3–4): 207–228 (1956).

    MathSciNet  MATH  Google Scholar 

  388. A. Moor, “Entwicklung einer Geometrie der allgemeinen metrischen Linienele-menträume,” Acta Sci. Math., 17(1–2): 85–120 (1956).

    MathSciNet  MATH  Google Scholar 

  389. A. Moór, “Über die Torsions- und Krümmungsinvarianten der dreidimensionalen Finslerschen Räume.,” Math. Nachr., 16(2): 85–99 (1957).

    MathSciNet  MATH  Google Scholar 

  390. A. Moor, “Über den Schurschen Satz in allgemeinen metrischen Linienele-menträumen,” Proc. Koninkl. Ned. Akad. Wetenschap., A60(3): 290–301 (1957);

    MathSciNet  Google Scholar 

  391. A. Moor, “Über den Schurschen Satz in allgemeinen metrischen Linienele-menträumen,” Indagationes Math., 19(3): 290–301 (1957).

    MathSciNet  Google Scholar 

  392. A. Moor, “Über die autoparallele Abweichung in allgemeinen metrischen Linienelementräumen,” Publ. Math., 5(1–2): 102–118 (1957).

    MathSciNet  MATH  Google Scholar 

  393. A. Moor, “Konformgeometrie der verallgemeinerten Schouten-Haantjesschen Räume. I,” Proc. Koninkl. Ned. Akad. Wetenschap., A61(1): 94–102 (1958);

    MathSciNet  Google Scholar 

  394. A. Moor, “Konformgeometrie der verallgemeinerten Schouten-Haantjesschen Räume. I,” Indagationes Math., 20(1): 94–102 (1958).

    MathSciNet  Google Scholar 

  395. A. Moor, “Konformgeometrie der verallgemeinerten Schouten-Haantjesschen Räume. II,” Proc. Koninkl. Ned. Akad. Wetenschap., A61(1): 103–113 (1958);

    Google Scholar 

  396. A. Moor, “Konformgeometrie der verallgemeinerten Schouten-Haantjesschen Räume. II,” Indagationes Math., 40(1): 103–113 (1958).

    MathSciNet  Google Scholar 

  397. A. Moor, “Über nichtholonome allgemeine metrische Linienelementräume,” Acta Math., 101(3–4): 201–233 (1959).

    MathSciNet  MATH  Google Scholar 

  398. A. Moor, “Erweiterung des Begriffs der Räume skalarer und konstanter Krümmung,” Acta Sci. Math., 21(1–2): 53–77 (1960).

    MathSciNet  MATH  Google Scholar 

  399. A. Moor, “Untersuchungen über die kovariante Ableitung in Linienelementen-räumen,” Publ. Math., 7(1–4): 41–53 (1960).

    MathSciNet  MATH  Google Scholar 

  400. A. Moor, “Über affine Finslerräume von skalarer Krümmung,” Acta Sci. Math., 22(3–4): 157–189 (1961).

    MathSciNet  MATH  Google Scholar 

  401. A. Moor, “Über die Form der Fundamentalgrössen gewisser affiner Räume,” Publ. Math., 9(3–4): 289–297 (1962).

    MathSciNet  MATH  Google Scholar 

  402. A. Moor, “Über projektive Veränderung der Übertragung in Linienelement-mannigfaltigkeiten,” Acta Sci. Math., 24(1–2): 119–128 (1963).

    MathSciNet  MATH  Google Scholar 

  403. A. Moor, “Untersuchungen über Finslerräume von rekurrenter Krümmung,” Tensor, 13:1–8 (1963).

    MathSciNet  MATH  Google Scholar 

  404. A. Moor, “Eine Verallgemeinerung der metrischen Übertragung in allgemeinen metrischen Räumen,” Publ. Math., 10(1–4): 145–150 (1963).

    MathSciNet  Google Scholar 

  405. A. Moor, “Untersuchungen über die oskulierenden Punkträume der metrischen Linienelementräume,” Liet. Matern. Rinkinys., 3(2): 212–213 (1963).

    Google Scholar 

  406. A. Moor, “Gleichung der autoparallelen Abweichung in n-dimensionalen Linienelementräumen,” Acta Sci. Math., 25(3–4): 266–282 (1964).

    MathSciNet  MATH  Google Scholar 

  407. A. Moor, “Untersuchungen über die oskulierenden Punkträume der metrischen Linienelementräume,” Acta Math. Acad. Sci. Hung., 16(1–2): 57–74 (1956).

    MathSciNet  Google Scholar 

  408. A. Moor, “Linienelementräume mit nicht-symmetrischem Fundamentaltensor,” Publ. Math., 11(1–4): 245–256 (1964).

    MathSciNet  Google Scholar 

  409. A. Moor, “Über eine skalare Form der Gleichung der autoparallelen Abweichung im affinem Raum,” Publ. Math., 12(1–4): 281–291 (1965).

    MathSciNet  MATH  Google Scholar 

  410. A. Moor, “Begründung einer affinen Geometrie der Bahnen dritter Ordnung,” Tensor, 16(1): 37–55 (1965).

    MathSciNet  MATH  Google Scholar 

  411. A. Moor, “Übertragungstheorie bezüglich der allgemeinen Linienelementen-transformationen,” Publ. Math., 13(1–4): 263–287 (1966).

    MathSciNet  MATH  Google Scholar 

  412. A. Moor and Gy. Soos “Über affinzusammenhängende Mannigfaltigkeiten von Hyperflächenelementen, insbesondere deren Aquivalenz,” Acta Sci. Math., 16(1–2): 29–42 (1955).

    MathSciNet  MATH  Google Scholar 

  413. Y. Muto and K. Yano, “Sur les transformations de contact et les espaces de Finsler,” Tohoku Math. J., 45: 295–307 (1939).

    Google Scholar 

  414. Y. Nagata, “Normal curvature of a vector field in a hypersurface in a Finsler space,” Tensor, 5(1): 17–22 (1955).

    MathSciNet  MATH  Google Scholar 

  415. Y. Nasu, “On the normality in Minkowskian spaces,” Kumamoto J. Sci., A2(1):11–17(1954).

    MathSciNet  Google Scholar 

  416. Y. Nasu, “On similarities in a Finsler space,” Tensor, 9(3): 175–189 (1959).

    MathSciNet  MATH  Google Scholar 

  417. A. Nazim, “Über Finslersche Räume,” Dissertation, Munich (1936).

    Google Scholar 

  418. A. Nazim, “Über den Satz von Gauss-Bonnet im Finslerschen Raum,” University of Instanbul (1948), pp. 26–32.

    Google Scholar 

  419. E. Noether, “Invarianten beliebiger Differentialausdrücke,” Gött. Nachr., 25:37–44(1918).

    Google Scholar 

  420. E. Noether, “Invarianten beliebiger Differentialausdrücke,” Jahresber. Deutsch. Mach.-Ver., 32:177–184 (1923).

    MATH  Google Scholar 

  421. T. Ohkubo, “Geometry in a space with generalized metrics. II,” J. Fac. Sci. Hokkaido Univ., Ser. I, 10:157–178 (1941).

    MathSciNet  Google Scholar 

  422. T. Ohkubo, “On a symmetric displacement in a Finsler space,” Tensor, 4: 53–55(1941).

    MathSciNet  Google Scholar 

  423. T. Ohkubo, “Descriptive geometry of paths” Tensor, 5: 81–86 (1942).

    MathSciNet  Google Scholar 

  424. T. Ohkubo, “A generalization of Cartan space,” Tensor, 6:45–48 (1943).

    MathSciNet  Google Scholar 

  425. T. Ohkubo, “Über die Extensorrechnung in den verallgemeinerten Räumen von Flächenelementen höherer Ordnung,” J. Fac. Sci. Hokkaido Univ., Ser. I, 11:1–37 (1946).

    MathSciNet  Google Scholar 

  426. T. Ohkubo, “On relations among various connections in Finslerian space,” Kumamoto J. Sci., A1(3):1–6 (1954).

    MathSciNet  Google Scholar 

  427. T. Ohkubo, “On the order of the groups of affine collineations in the generalized spaces of paths. I, II, III,” Tensor, 6(3): 141–158 (1956);

    MathSciNet  Google Scholar 

  428. T. Ohkubo, “On the order of the groups of affine collineations in the generalized spaces of paths. I, II, III,” Tensor, 7(1): 1–17 (1957);

    MathSciNet  Google Scholar 

  429. T. Ohkubo, “On the order of the groups of affine collineations in the generalized spaces of paths. I, II, III,” Tensor, 7(1): 18–33 (1957).

    MathSciNet  Google Scholar 

  430. M. Okumura, “On some remarks of special Kawaguchi spaces,” Tensor 11(2): 154–160 (1961).

    MathSciNet  MATH  Google Scholar 

  431. T. Otsuki, “On geodesic coordinates in Finsler spaces,” Math. J. Okayama Univ., 6(2):135–145 (1957).

    MathSciNet  MATH  Google Scholar 

  432. T. Otsuki, “Theory of affine connections of the space of tangent directions of a differentiable manifold. I, II,” Math. J. Okayama Univ., 7(1): 1–74(1957).

    MathSciNet  Google Scholar 

  433. T. Otsuki, “Theory of affine connections of the space of tangent directions of a differentiable manifold. III,” Math. J. Okayama Univ., 7(2): 95–122 (1957).

    Google Scholar 

  434. T. Otsuki, “Note on curvature of Finsler manifolds,” Math. J. Okayama Univ., 8(2):102–116 (1958).

    Google Scholar 

  435. O.G. Owens, “The integral geometry definition of arc-length for two-dimensional Finsler spaces,” Trans. Am. Math. Soc., 73:198–210 (1952).

    MathSciNet  MATH  Google Scholar 

  436. M. Pihl, “Classical mechanics in a geometrical description,” Danske Vid. Selsk. Math.-Fys. Medd., Vol. 30, No. 12 (1955).

    Google Scholar 

  437. N. Prakash, “Generalised normal curvature of a curve and generalised principal directions in Finsler space,” Tensor, 11(1): 51–56 (1961).

    MathSciNet  MATH  Google Scholar 

  438. N. Prakash, “Kählerian Finsler manifolds,” Math. Student, 30(1–2): 1–12(1962).

    MathSciNet  MATH  Google Scholar 

  439. N. Prakash and Ram Behari, “Deviations from parallelism and equidistance in Finsler space,” Proc. Indian Acad. Sci., A52(5): 209–227 (1960).

    Google Scholar 

  440. N. Prakash and Ram Behari, “Generalizations of Codazzi’s equations in a subspace imbedded in a Finsler manifold,” Proc. Nat. Inst. Sci., India, A26(5): 532–540 (1960).

    MathSciNet  Google Scholar 

  441. N. Prakash and R. Behari, “Union curves and union curvature in Finsler space,” Proc. Nat. Inst. Sci., India, A26, Suppl., No. 2, pp. 21–30 (1960).

    MathSciNet  Google Scholar 

  442. A. Rapscak, “A normalkoordinatak egy uj ertelmezése a finsler terben,” Acta Univ. Debrecen, 1:109–116 (1954).

    MathSciNet  Google Scholar 

  443. A. Rapscak, “Theorie der Bahnen in Linienelementmannigfaltigkeiten und eine Verallgemeinerung ihrer affinen Theorie,” Acta Sci. Math., 16(3–4): 251–265 (1955).

    Google Scholar 

  444. A. Rapscak, “Invariante Taylorsche Reihe in einem Finslerschen Raum,” Publ. Math., 4(1–2): 49–60 (1955).

    Google Scholar 

  445. A. Rapscak, “Über das vollständige System von Differentielinvarianten im regulärer Cartanschen Raum,” Publ. Math., 4(3–4): 276–293 (1956).

    Google Scholar 

  446. A. Rapscak, “Eine neue Charakterisierung Finslerscher Räume skalarer und konstanter Krümmung und projectiv-ebene Räume,” Acta Math. Acad. Sci. Hung., 8(1–2): 1–18 (1957).

    Google Scholar 

  447. A. Rapscak, “Metrische Charakterisierung der Finslerschen Räume mit verschwindender projectiver Krümmung,” Acta Sci. Math., 18(3–4):192–204 (1957).

    Google Scholar 

  448. A. Rapscak, “Hypersikok a Finsler-féle terben,” Acta Univ. Debrecen, 4:85–87 [1957 (1959)].

    Google Scholar 

  449. A. Rapscak, “Metricus és affinösszefüggö pályaterek pályatartá leképezései,” Magy. Tud. Akad. Mat. Fiz. Tud. Oszt. Kozleman., 11(4):339–369 (1961).

    Google Scholar 

  450. A. Rapscak, “Über die bahntreuen Abbildungen metrischer Räume,” Publ. Math., 8(3–4): 285–290 (1961).

    Google Scholar 

  451. A. Rapscak, “Die Bestimmung der Grundfunktionen projectiv-ebener metrischer Räume,” Publ. Math., 9(1–2): 164–167 (1962).

    Google Scholar 

  452. A. Rapscak, “Über die Metrisierbarkeit affinzusammenhängender Bahnräume,” Ann. Mat. Pura ed Appl., 57:233–238 (1962).

    Google Scholar 

  453. P. Rashevskii (Rashevsky), “Une géometrie métrique quale, fondée sur les espaces de Cartan généralisés,” Compt. Rend. Acad. Sci., Paris, (1935), pp. 921–923.

    Google Scholar 

  454. P. Rashevskii (Rashevsky), “Système bimétrique dual,” Compt. Rend. Acad. Sci. Paris, 201:1088–1090 (1935).

    Google Scholar 

  455. P. Rashevskii (Rashevsky), “Systèmes trimétriques et la métrique de Finsler Généralisée,” Compt. Rend. Acad. Sci., Paris, 202:1237–1239 (1936).

    Google Scholar 

  456. Georges Reeb, “Sur les espaces de Finsler et les espaces de Cartan,” in: Colloq. Intern. Centre Nat. Rech. Sci., 52, Strasbourg, 1953, Paris (1953), pp. 35–40.

    Google Scholar 

  457. G. B. Rizza, “Strutture de Finsler sulle varieta quasi complesse,” Atti Accad. Naz. Lincei Rend. Cl. Sci. Fiz. Mat. Nat., 33(5): 271–275 [1962 (1963)]. (1963)].

    MATH  Google Scholar 

  458. G. B. Rizza, “Strutture di Finsler di tipo quasi hermitiano,” Riv. Mat. Univ. Parma, 4:83–106 (1963).

    MathSciNet  MATH  Google Scholar 

  459. H. Rund, “Die Hamiltonsche Funktion bei allgemeinen dynamischen Systemen,” Arch. Math., 3:207–215 (1952).

    MathSciNet  MATH  Google Scholar 

  460. H. Rund, “On the geometry of generalized metric spaces,” Convegno Internazionale di Geometria Differenziale, Italy, 1953, Ed. Cremonese, Rome (1954), pp. 114–121.

    Google Scholar 

  461. H. Rund, “On the analytical properties of curvature tensors in Finsler spaces,” Math. Ann., 127(1): 82–104 (1954).

    MathSciNet  MATH  Google Scholar 

  462. H. Rund, “Über nicht-holonome allgemeine metrische Geometrie,” Math. Nachr., 11(1–2): 61–80 (1954).

    MathSciNet  MATH  Google Scholar 

  463. H. Rund, “Hypersurfaces of a Finsler space,” Can. J. Math., 8(4): 487–503 (1956).

    MathSciNet  MATH  Google Scholar 

  464. H. Rund, “Some remarks concerning the theory of nonlinear connections,” Proc. Koninkl. Ned. Akad. Wetenschap., A61(3): 341–347 (1958)

    MathSciNet  Google Scholar 

  465. H. Rund, “Some remarks concerning the theory of nonlinear connections,” Indagationes Math., 20(3): 341–347 (1958).

    MathSciNet  Google Scholar 

  466. H. Rund, The Differential Geometry of Finsler Spaces, Spinger, Berlin (1959), XIII, p. 283.

    MATH  Google Scholar 

  467. H. Rund, “Über Finslersche Räume mit speziellen Krümmungseigenschaften,” Monatsh. Math., 66(3): 241–251 (1962).

    MathSciNet  MATH  Google Scholar 

  468. H. Rund, “Curvature properties of hypersurfaces of Finsler and Minkowskian spaces,” Tensor, 14:226–244(1963).

    MathSciNet  MATH  Google Scholar 

  469. H. Rund, “The intrinsic and induced curvature theories of subspaces of a Finsler space,” Tensor, 16(3): 294–312 (1965).

    MathSciNet  MATH  Google Scholar 

  470. S. Sasaki, “On some properties in the large in the geometry of paths,” Tensor, 8:41–53 (1948).

    MathSciNet  Google Scholar 

  471. H. Sasayama, “On the nonholonomic quasi-Euclidean space of line-elements,” J. Spat. Math. Sasayama Res. Room, 4(2–3): 62–88 (1961).

    Google Scholar 

  472. J. A. Schouten and J. Haantjes, “Über die Festlegung von allgemeinen Massbestimmungen und Übertragungen in Bezug auf k0 und kontravariante Vektor-dichten,” Monatsh. Math. Phys., 43:161–176 (1936).

    MathSciNet  Google Scholar 

  473. V. Seetharaman, “Differential invariants for path-space of order 2,” Proc. Indian Acad. Sci., A5:161–165 (1937).

    Google Scholar 

  474. B. Segre, “Geometria non euclidea ed ottica geometrica. I, II,” Atti Accad. Naz. Lincei, Rend. C1. Sci. Fis., Mat. Nat., 8(7): 16–19 (1949)

    Google Scholar 

  475. B. Segre, “Geometria non euclidea ed ottica geometrica. I, II,” Atti Accad. Naz. Lincei, Rend. C1. Sci. Fis., Mat. Nat., 8(7): 20–26 (1949).

    Google Scholar 

  476. R. N. Sen, “Application of an algebraic system in Finsler geometry,” Tensor, 18(2): 191–195 (1967).

    MathSciNet  MATH  Google Scholar 

  477. R. N. Sen, “On curvature tensors in Finsler geometry,” Tensor, 18(2): 217–226 (1967).

    MathSciNet  MATH  Google Scholar 

  478. A. C. Shamihoke, “On the subspaces of a Finsler space,” J. Indian Math. Soc, 25(3–4):215–220 (1961).

    MathSciNet  Google Scholar 

  479. A. C. Shamihoke, “Some properties of curvature tensors in a generalised Finsler space,” Tensor, 12(2): 97–109 (1962).

    MathSciNet  MATH  Google Scholar 

  480. A.C. Shamihoke, “Normal curvature of a vector field in a hypersurface of a generalised Finsler space,” Istanbul Univ. Fen. Fak. Mecmuasi, A27: 9–14 (1962).

    MathSciNet  Google Scholar 

  481. A. C. Shamihoke, “Subspaces of a generalised Finsler space. I,” Ganita, 14(1): 43–59 (1963).

    MathSciNet  MATH  Google Scholar 

  482. A. C. Shamihoke, “Hypersurfaces of a generalised Finsler space,” Tensor, 13:129–144(1963).

    MathSciNet  MATH  Google Scholar 

  483. A. C. Shamihoke, “A note on a curvature tensor in a Finsler space,” Tensor, 15(1): 20–22 (1964).

    MathSciNet  MATH  Google Scholar 

  484. A.C. Shamihoke, “Parallelism and covariant differentiation in a generalized Finsler space of n dimensions,” Riv. Mat. Univ. Parma, 5:189–200 (1964).

    MathSciNet  MATH  Google Scholar 

  485. E. B. Shanks, “Homothetic correspondences between Riemannian spaces,” Duke Math. J., 17:299–311 (1950).

    MathSciNet  MATH  Google Scholar 

  486. N. K. Sharma and R. Behari, “Some properties of spaces with the arc length s = ∫{A i x i , x i ) x i }) 1/3 dt,” Ganita, 15(1): 1–8 (1964).

    MathSciNet  MATH  Google Scholar 

  487. B. B. Sinha, “Projective invariants,” Math. Student, 33(2–3): 121–127 (1965).

    MathSciNet  MATH  Google Scholar 

  488. W. Slebodzinski, “Sur deux connexions affines généralisées,” Prace Mat.-Fizycz., 43:167–205(1935).

    Google Scholar 

  489. Gy. Soôs, “Über Gruppen von Affintäten und Bewegungen in Finslerschen Räumen,” Acta Math. Acad. Sci. Hung., 5(1–2): 73–84 (1954).

    MATH  Google Scholar 

  490. Gy. Soôs, “Über Gruppen von Automorphismen in affinzusammenhängenden Räumen von Linienelementen,” Publ. Math., 4(3–4): 294–302 (1956).

    MATH  Google Scholar 

  491. Gy. Soôs, “Über eine spezielle Klasse von Finslerschen Räumen,” Publ. Math., 5(1–2): 150–153 (1957).

    Google Scholar 

  492. Gy. Soôs, “Über die nomothetische Gruppe von Finslerschen Räumen,” Acta Math. Acad. Sci. Hung., 10(3–4): 391–394 (1959).

    MATH  Google Scholar 

  493. Gy. Soôs, “Über einfache Finslersche Räume,” Publ. Math., 7(1–4): 364–373 (1960).

    MathSciNet  MATH  Google Scholar 

  494. Gy. Soôs, “A Finsler-féle fibrált terek elméletéhez,” Magy. Tud. Akad. Mat. Fiz. Tud. Oszt. Közlemen., 13(1): 17–64 (1963).

    MATH  Google Scholar 

  495. T. N. Srivastava, “A few remarks on special Kawaguchi spaces,” Tensor, 15(1): 12–19 (1964).

    MathSciNet  MATH  Google Scholar 

  496. Buchin Su, “On the isomorphic transformations of K-spreads in a Douglas space,” Acad. Sinica Sci. Record, 2:11–19 (1947).

    MATH  Google Scholar 

  497. Buchin Su, “On the isomorphic transformations of K-spreads in a Douglas space. n,” Acad. Sinica Sci. Record, 2:139–146 (1948).

    MATH  Google Scholar 

  498. Buchin Su, “A characteristic property of affine collineations in a space of K-spreads,” Bull. Am. Math. Soc, 54:136–138 (1948).

    MATH  Google Scholar 

  499. Buchin Su, “Geodesic deviation in generalized metric spaces,” Acad. Sinica Sci. Record, 2:220–226 (1949).

    MATH  Google Scholar 

  500. Buchin Su, “Axiom of the plane in a space of K-spreads,” Acad. Sinica Sci. Record, 3:7–16 (1950).

    MATH  Google Scholar 

  501. Buchin Su, “A generalization of descriptive collineations in a space of K-spreads,” J. London Math. Soc, 25:236–238 (1950).

    MathSciNet  MATH  Google Scholar 

  502. Buchin Su, “Extremal deviation in a geometry based on the notion of area,” Acta Math., 85: 99–116 (1951).

    MathSciNet  MATH  Google Scholar 

  503. Buchin Su, “Koschmider invariant and the associate differential equation of a minimal hypersurface in a regular Cartan space,” Math. Nachr., 16:117–129 (1957).

    MathSciNet  Google Scholar 

  504. Buchin Su, “Axiom of the plane in a descriptive geometry of K-spreads,” Math. Nachr., 16(3–4): 215–226 (1957).

    MathSciNet  MATH  Google Scholar 

  505. Buchin Su, “A generalization of descriptive collineations in a space of K-spreads,” Math. Nachr., 16(3–4): 227–232 (1957).

    MathSciNet  MATH  Google Scholar 

  506. Buchin Su, “On the determination of certain affine connections in an areal space,” Sci. Rec, 1(4): 195–198 (1957).

    MATH  Google Scholar 

  507. Buchin Su, “The geometry of spaces with areal metrics,” Math. Nachr., 16(5–6): 281–287 (1957).

    MathSciNet  MATH  Google Scholar 

  508. Buchin Su, “Certain affinely connected spaces with areal metrics,” Scientia Sinica, 6(6): 967–975 (1957).

    MathSciNet  MATH  Google Scholar 

  509. Buchin Su, “Recent progress in the differential geometry of a space of K-spreads,” in: Lucrǎrile Conf. Geometrie Si Topol., 1958, Acad. RPR, Bucurest (1962), pp. 21–30.

    Google Scholar 

  510. Buchin Su, “On the theory of affine connections in an areal space,” Bull. Math. Soc, Sci. Math, et Phys. (RPR), 2(2): 185–190 (1958).

    Google Scholar 

  511. Buchin Su and Chaohao Ku, “The developments of differential geometry in China for the past ten years,” Scientia Sinica, 8(11): 1238–1242 (1959).

    MathSciNet  MATH  Google Scholar 

  512. T. Suguri, “Theory of invariants in the geometry of paths,” J. Math. Soc. Japan, 4:231–268 (1952).

    MathSciNet  MATH  Google Scholar 

  513. R. Sulanke, “Die eindeutige Bestimmtkeit des von Hanno Rund eigeführten Zusammenhangs in Finsler-Räumen,” Wiss. Z. Humboldt-Univ. Berlin, Math.-Naturwiss. Reihe, 4(4): 229–233 (1954).

    MathSciNet  Google Scholar 

  514. R. Sulanke, “Anmerkung zu der Arbeit: ‘Die eindeutige Bestimmtheit des von Hanno Rund eigeführten Zusammenhangs in Finsler-Räumen’,” Wiss. Z. Humboldt-Univ. Berlin, Math.-Naturwiss. Reihe, 5(3): 269 (1955/56).

    Google Scholar 

  515. R. Sulanke, “Eine Ableitung des Cartanschen Zusammenhangs eines Finsler-schen Raumes,” Publ. Math., 5(1–2): 197–203 (1957).

    MathSciNet  MATH  Google Scholar 

  516. W. Süss, “Affine und Minkowskische Geometrie eines ebenen Variations-problems,” Arch. Math., No. 4–6, pp. 441–446 (1954).

    Google Scholar 

  517. Y. Suzuki, “Finsler geometry in classical physics,” J. Coll. Arts Sci. Chiba Univ. Natur. Sci. Ser., 2(1): 12–16 (1956).

    Google Scholar 

  518. S. L. Synge, “A generalization of the Riemannian line element,” Trans. Am. Math. Soc, 27:61–67 (1925).

    MathSciNet  MATH  Google Scholar 

  519. S. L. Synge, “Some intrinsic and derived vectors in a Kawaguchi space,” Am. J. Math., 57:679–691 (1935).

    MathSciNet  Google Scholar 

  520. Syunichi Tachibana, “On Finsler spaces which admit a concurrent vector field,” Tensor, 1:1–5 (1950).

    MathSciNet  MATH  Google Scholar 

  521. K. Tandai, “On areal spaces. VI. On the characterization of metric areal spaces,” Tensor, 3: 40–45 (1953).

    MathSciNet  MATH  Google Scholar 

  522. K. Tandau, “On areal spaces. VII. The theory of the canonical connection and m-dimensional subspaces,” Tensor, 4(2): 78–90 (1954).

    MathSciNet  Google Scholar 

  523. K. Tandau, “On areal spaces. VIII. Theory of a space of the semi-metric class,” Tensor, 10:161–166 (1960).

    MathSciNet  Google Scholar 

  524. K. Tandau, “On general connections in an areal space. I. General connection on a fibre of the tangent m-frame bundle,” Tensor, 13: 277–291 (1963).

    MathSciNet  Google Scholar 

  525. K. Tandau, “On general connections in an areal space. II. On general connections on the tangent m-frame bundle,” Tensor, 14: 26–46 (1963).

    MathSciNet  Google Scholar 

  526. Y. Tashiro, “A theory of transformation groups on generalized spaces and its applications to Finsler and Cartan spaces,” J. Math. Soc. Japan, 11(1): 42–71 (1959).

    MathSciNet  MATH  Google Scholar 

  527. J. H. Taylor, “A generalization of Levi-Civita’s parallelism and the Frenet formulas,” Trans. Am. Math. Soc, 27:246–264 (1925).

    MATH  Google Scholar 

  528. N. Théodoresci, “Sur les géodésiques de longeur nulle de certains éléments lineaires finslériens,” Bull. École Polytech. Bucarest, 12:9–16 (1941).

    Google Scholar 

  529. N. Théodoresci, “Géométrie finslérienne et propagation des ondes,” Acad. Roumaine Bull. Sec. Sci., 23:138–144 (1942).

    Google Scholar 

  530. N. Théodoresci, “Introduction physico-mathématique a la théorie invariante de la propagation des ondes,” Rev. Univ. si Politechn. Bucuresti, Ser. Stint. Natur., 1:25–51 (1952).

    Google Scholar 

  531. N. N. Teodorescu, “Asupra unor spatii Finsler,” Studii Si Cercetari Mat. Acad. RPR, 13(3): 499–510 (1962).

    MathSciNet  MATH  Google Scholar 

  532. K. Tonooka, “Generalized rheonomic geometry of K-spreads,” Tensor, 3:26–39(1953).

    MathSciNet  MATH  Google Scholar 

  533. K. Tonooka, “Theory of subspaces in a geometry based on a multiple integral. I. Metric tensor and theory of connections,” Tensor, 4: 75–83 (1954).

    Google Scholar 

  534. K. Tonooka, “On intrinsic theories in the manifold of surface elements of higher order. II. Intrinsic geometry of a system of partial differential equations,” Tensor, 4(2): 67–77 (1954).

    MathSciNet  MATH  Google Scholar 

  535. K. Tonooka, “On a geometry of three-dimensional space with an algebraic metric,” Tensor, 6(1): 60–68 (1956).

    MathSciNet  MATH  Google Scholar 

  536. K. Tonooka, “On three- and four-dimensional Finsler spaces with the fundamental form \(\sqrt[3]{{{a_{\alpha \beta \gamma }}{{x'}^\alpha }{{x'}^\beta }{{x'}^\gamma }}}\),” Tensor, 9(3): 209–216 (1959).

    MathSciNet  MATH  Google Scholar 

  537. K. Tonowoka, “On a metric displacement along a curve in a special Kawaguchi space,” Tensor, 4: 60–62 (1941).

    MathSciNet  Google Scholar 

  538. K. Tonowoka, “On a geometrical treatment of an (n-1)-ple integral of some kind,” Tensor, 7:16–23 (1944).

    MathSciNet  Google Scholar 

  539. K. Tonowoka, “On invariants of \(\int_{(n - 1)} {{{\left\{ {A_{ij}^{\alpha (2)\beta (3)}p_{\beta (3)}^j + B_j^{\beta (3)}p_{\beta (3)}^j + C} \right\}}^{1/p}}} d{u^1} \ldots d{u^{n - 1}}\),” Tensor, 9:18–24(1949).

    MathSciNet  Google Scholar 

  540. K. Tonowoka, “A problem on the generalization of Cartan space,” Sugeku Jap. Math. Soc., 2:47–50 (1950).

    Google Scholar 

  541. T. N. Srivastava, “Les identités généralisées de Bianchi et de Veblen dans les espaces de Kawaguchi spéciaux,” Compt. Rend. Acad. Sci., Paris, 254(15): 2706–2708 (1962).

    MATH  Google Scholar 

  542. T. Uehara, “The discontinuous character of the three-dimensional motion of a compressible fluid in terms of the geometry of Cartan space,” RAAG Mem. Unifying Study Basic Probl. Engng. and Phys., Sci. Means Geom., Vol. 3, Tokyo Gakujutsu Bunken Fukyu-kai (1962), pp. 735–742.

    Google Scholar 

  543. S. Ueno, “On the densities in a two-dimensional generalized space,” Mem. Fac. Sci. Kyusyu Univ., A9(1): 65–77 (1955).

    MathSciNet  Google Scholar 

  544. A. Urban, “On the geometry of a system of partial differential equations of the second order,” Proc. Koninkl. Ned. Akad. Wetenschap., A52: 855–867 (1949)

    MathSciNet  Google Scholar 

  545. A. Urban, “On the geometry of a system of partial differential equations of the second order,” Indagationes Math., 11:303–315 (1949).

    Google Scholar 

  546. J. R. Vanstone, “A generalization of Finsler geometry,” Can. J. Math., 14(1): 87–112 (1962).

    MathSciNet  MATH  Google Scholar 

  547. O. Varga, “Bestimmung des invarianten Differentials in Finslerschen Räumen,” Math.-Fiz. Lapok, 48:423–435 (1941).

    Google Scholar 

  548. O. Varga, “Aufbau der Finslerschen Geometrie mit Hilfe einer oskulierenden Minkowskischen Massbestimmung,” Math. Nat. Anz. Ungarn. Acad. Wiss., 61:14–22 (1942).

    Google Scholar 

  549. O. Varga, “Zur Begründung der Minkowskischen Geometrie,” Acta Univ. Szeged. Sec. Ser. Math., 10:149–163 (1943).

    MATH  Google Scholar 

  550. O. Varga, “Olyan finsler-terek jellemzése, amelyekben létezik a vonalemek abszolut parhuzamossaga,” Acta Univ. Debrecen, 1:105–108 (1954).

    MathSciNet  Google Scholar 

  551. O. Varga, “Eine Charakterisierung der Finslerschen Räume mit absolutem Parallelismus der Linienelemente,” Arch. Math., 5(1–3): 128–131 (1954).

    MATH  Google Scholar 

  552. O. Varga, “Bedingungen für die Metrisierbarkeit von affinzusammenhängenden Linienelementmannigfaltigkeiten,” Acta Math. Acad. Sci. Hung., 5(1–2): 7–16 (1954).

    MATH  Google Scholar 

  553. O. Varga, “Die Krümmung der Eichfläche des Minkowskischen Raumes und die geometrische Deutung des einen Krümmungstensors des Finslerschen Raumes,” Abhandl. Math. Seminar Univ. Hamburg, 20(1–2): 41–59 (1955).

    MATH  Google Scholar 

  554. O. Varga, “Eine Charakterisierung der Kawaguchischen Räume metrischer Klasse mittels eines Satzes über derivierte Matrizen,” Publ. Math., 4(3–4): 418–430 (1956).

    MATH  Google Scholar 

  555. O. Varga, “Normalkoordinaten in Kawaguchischen Räumen und seine affinen Verallgemeinerungen sowie eine Anwendung derselben zur Bestimmung von Differentialinvarianten,” Math. Nachr., 18(1–6): 141–151 (1958).

    MathSciNet  MATH  Google Scholar 

  556. O. Varga, “Über die Zerlegbarkeit von Finslerschen Räumen,” Acta math. Acad. Sci. Hung., 11(1–2): 197–203 (1960).

    MATH  Google Scholar 

  557. O. Varga, “Bemerkung zur Winkelmetrik in Finslerschen Räumen,” Ann. Univ. Sci. Budapest, Sec. Math., 3–4:379–382 (1960–1961).

    Google Scholar 

  558. O. Varga, “Über eine Charakterisierung der Finslerschen Räume konstanter Krümmung,” Monatsh. Math., 65(3): 277–286 (1961).

    MathSciNet  MATH  Google Scholar 

  559. O. Varga, “Herleitung des Cartanschen euklidischen Zusammenhanges in Finslerräumen mit Hilfe der Riemannschen Geometrie,” Acta Univ. Debrecen, Ser. Phys. et Chim., 8:121–124 (1962).

    Google Scholar 

  560. O. Varga, “Eine einfache Herleitung der Cartanschen Übertragung der Finsler-geometrie,” Math. Notae, 18(1): 185–196 (1962).

    MathSciNet  Google Scholar 

  561. O. Varga, “Über Hyperflächen konstanter Normalkümmung in Minkowskischen Räumen,” Tensor, 13:246–250 (1963).

    MathSciNet  MATH  Google Scholar 

  562. O. Varga, “Hyperflächen mit Minkowskischer Massbestimmung in Finslerräumen,” Publ. Math., 11(1–4): 301–309 (1964).

    MATH  Google Scholar 

  563. O. Varga, “Die Methode des beweglichen n-Beines in der Finsler-Geometrie,” Acta Math. Acad. Sci. Hung., 18(1–2): 207–215 (1967).

    MATH  Google Scholar 

  564. O. Veblen, “Normal coordinates for the geometry of paths,” Proc. Nat. Acad. Sci. USA, 8:192–197 (1922).

    Google Scholar 

  565. O. Veblen, “Equiaffine geometry of paths,” Proc Nat. Acad. Sci. USA, 9:3–4 (1923).

    Google Scholar 

  566. O. Veblen, “Generalized projective geometry,” J. Lond. Math. Soc, 4:140–160 (1929).

    MATH  Google Scholar 

  567. O. Veblen and T. Y. Thomas, “The geometry of paths,” Trans. Am. Math. Soc, 25:551–608 (1923).

    MathSciNet  Google Scholar 

  568. O. Veblen and T. Y. Thomas, “Projective normal coordinates for the geometry of paths,” Proc Nat. Acad. Soc, 11: 204–207 (1925).

    MATH  Google Scholar 

  569. O. Veblen and T. Y. Thomas, “Projective invariants of affine geometry of paths,” Ann. Math., 27:278–296 (1926).

    MathSciNet  Google Scholar 

  570. Vaclav Vinhelm, “Krivky v prostorèch Minkowského,” Casop. Pestov. Mat., 82(3): 283–300 (1957).

    Google Scholar 

  571. V. V. Vagner (Wagner), “Geometria del calcolo delle variationi,” Centro Intern. Mat. Estivo (1965).

    Google Scholar 

  572. Hsien-Chung Wang, “On Finsler spaces with completely integrable equations of Killing,” J. Lond. Math. Soc., 22: 5–9 (1947).

    MATH  Google Scholar 

  573. Yuen-da Wang, “Finsler spaces of constant curvature and totally extremal hy-persurf aces,” Sci. Rec, 2(7): 211–214 (1958).

    MATH  Google Scholar 

  574. S. Watanabe, “On special Kawaguchi spaces,” Tensor, 7(2):130–136 (1957).

    MathSciNet  MATH  Google Scholar 

  575. Shoji Watanabe, “On special Kawaguchi spaces. II,” Tensor, 8(3): 69–176 (1958).

    Google Scholar 

  576. S. Watanabe, “On special Kawaguchi spaces. III. Generalizations of affine spaces and Finsler spaces,” Tensor, 11(2): 144–153 (1961).

    MathSciNet  MATH  Google Scholar 

  577. S. Watanabe, “On special Kawaguchi spaces. IV. Extremal curves in the generalized affine spaces,” Tensor, 11(3): 254–262 (1961).

    MathSciNet  Google Scholar 

  578. S. Watanabe, “On special Kawaguchi spaces. V. Some remarks on the special Kawaguchi spaces,” Tensor, 11(3): 279–284 (1961).

    MathSciNet  Google Scholar 

  579. S. Watanabe, “On special Kawaguchi spaces. VI. Some transformations in certain special Kawaguchi spaces,” Tensor, 12(3): 244–253 (1962).

    MathSciNet  MATH  Google Scholar 

  580. S. Watanabe and M. Yoshida, “On special Kawaguchi spaces. VII. Some transformations in certain special Kawaguchi spaces H,” Tensor, 13:31–41 (1963).

    MathSciNet  MATH  Google Scholar 

  581. J. M. Wegener, “Untersuchung der zwei- und dreidimensionalen Räume mit der Grundfunktion (Math),” Proc. Koninkl. Ned. Akad. Wetenschap., Ser. A, 38:949–955 (1935).

    Google Scholar 

  582. J. M. Wegener, “Hyperflächen in Finslerschen Räumen als Transversalflächen einer Schar von Extremalen,” Monatsh. Math. Phys., 44:115–130 (1936).

    MathSciNet  Google Scholar 

  583. A. Winternitz, “Über die affine Grundlage der Metrik eines Variationsproblems,” Sitzber. Acad. Wiss. Berlin (1930), pp. 457–469.

    Google Scholar 

  584. W. Wrona, “On multi-isotropic Finsler spaces,” Bull. Acad. Polon. Sci. Ser. Sci. Math., Astron. Phys., 11(5): 285–288 (1963).

    MathSciNet  MATH  Google Scholar 

  585. W. Wrona, “A necessary and sufficient condition for the Finsler space with distant parallelism of line elements to be multi-isotropic,” Bull. Acad. Polon. Sci. Ser. Sci. Math., Astron. Phys., 11(5): 289–292 (1963).

    MathSciNet  MATH  Google Scholar 

  586. W. Wrona, “Generalized F. Schur theorem in Finsler spaces,” Bull. Acad. Polon. Sci. Ser. Sci. Math., Astron. Phys., 11(5): 293–295 (1963).

    MathSciNet  MATH  Google Scholar 

  587. A. Wundheiler, “Über Variationsgleichungen für affine geodätische Linien und nicht-holonome, nicht-konservative dynamische Systeme,” Prace Mat. Fiz., (1931), pp. 129–147.

    Google Scholar 

  588. K. Yano, Groups of Transformations in Generalized Spaces, Akad. Press, Tokyo (1949).

    Google Scholar 

  589. K. Yano, The Theory of Lie Derivatives and Its Applications, Amsterdam (1957), 299 pp.

    MATH  Google Scholar 

  590. K. Yano and H. Hiramatsu, “Affine and projective geometries of systems of hypersurfaces,” J. Math. Soc. Japan, 3:116–136 (1951).

    MathSciNet  MATH  Google Scholar 

  591. K. Yano and H. Hiramatsu, “On projective geometry of K-spreads,” Composition Math., 10:286–296 (1952).

    MATH  Google Scholar 

  592. K. Yano and H. Hiramatsu, “On groups of projective coUineations in a space of K-spreads,” J. Math. Soc. Japan, 6(2): 131–150 (1954).

    MathSciNet  MATH  Google Scholar 

  593. K. Yano and E. T. Davies, “On the connection in Finsler space as an induced connection,” Rend. Circolo Mat. Palermo, 3(3): 409–417 (1954).

    MathSciNet  MATH  Google Scholar 

  594. K. Yano and E. T. Davies, “On the tangent bundles of Finsler and Riemannian manifolds,” Rend. Circolo Mat. Palermo, 12(2): 221–228 (1963).

    MathSciNet  Google Scholar 

  595. M. Yoshida, “On the connections in a subspace of the special Kawaguch space,” Tensor, 17(1): 49–52 (1966).

    MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. V. I. Bliznikas
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, Moscow, Russia

    R. V. Gamkrelidze

Rights and permissions

Reprints and permissions

Copyright information

© 1971 Plenum Press, New York

About this chapter

Cite this chapter

Bliznikas, V.I. (1971). Finsler Spaces and Their Generalizations. In: Gamkrelidze, R.V. (eds) Progress in Mathematics. Progress in Mathematics, vol 9. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3306-7_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-3306-7_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-3308-1

  • Online ISBN: 978-1-4684-3306-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation