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Geometry of differential equations

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Literature cited

  1. S. I. Bilchev, “Systems of two first-order partial differential equations (local theory),” Izv. Vyssh. Uchebn. Zavedenii, Matematika, No. 3, 14–21 (1970).

    Google Scholar 

  2. S. I. Bilchev, “Systems of two first-order partial differential equations (conservation laws),” Izv. Vyssh. Uchebn. Zavedenii, Matematika, No. 6, 28–34 (1970).

    Google Scholar 

  3. S. I. Bilchev, “Systems of two first-order partial differential equations with two unknown functions and two independent variables (local theory),” Nauchn. Tr. Vyssh. Inst. Mashinostr., Mekhaniz. i Élektrifik. Sel'sk. Stop.-Ruse,12, No. 3, 21–27 (1972).

    Google Scholar 

  4. V. I. Bliznikas, “On certain manifolds of support elements,” Liet. Matem. Rinkinys,3, No. 2, 221–222 (1963).

    Google Scholar 

  5. V. I. Bliznikas, “Euclidean connection of Cartan type in a metric space of line elements,” Liet. Matem. Rinkinys,2, No. 2, 33–37 (1963).

    Google Scholar 

  6. V. I. Bliznikas, “Affine connection in a space of support elements,” Repts. Third Siberian Conf. Math. Mech., 1964 [in Russian], Tomskii Univ., Tomsk (1964), pp. 181–183.

    Google Scholar 

  7. V. I. Bliznikas, “Nonholonomic Lie differentiation and linear connections in a space of support elements,” Liet. Matem. Rinkinys,6, No. 2, 141–208 (1966).

    Google Scholar 

  8. V. I. Bliznikas, “Differential equations of certain fields of differential-geometric objects,” Liet. Matem. Rinkinys,6, No. 4, 497–501 (1966).

    Google Scholar 

  9. V. I. Bliznikas, “On the geometry of systems of higher-order differential equations,” Liet. Matem. Rinkinys,6, No. 4, 620 (1966).

    Google Scholar 

  10. V. I. Bliznikas, “On the geometry of normal systems of higher-order ordinary differential equations,” Liet. Matem. Rinkinys,7, No. 2, 231–248 (1967).

    Google Scholar 

  11. V. I. Bliznikas, “On the inner connections of fibered spaces associated with systems of differential equations,” in: Third Interinst. Sci. Conf. Prob. Geom. (Repts. Abstrs.) [in Russian], Kazan' (1967), pp. 17–18.

  12. V. I. Bliznikas, “On the geometry of systems of second-order partial differential equations,” Liet. Matem. Rinkinys,7, No. 2, 249–264 (1967).

    Google Scholar 

  13. V. I. Bliznikas, “Affine connections associated with a quasilinear system of first-order partial differential equations,” Izv. Vyssh. Uchebn. Zavedenii, Matematika, No. 1, 18–22 (1968).

    Google Scholar 

  14. V. I. Bliznikas, “Finsler spaces and their generalizations,” in: Progress in Mathematics, Vol. 9: Algebra and Geometry (edited by R. V. Gamkrelidze), Plenum Press, New York-London (1971), pp. 75–136.

    Google Scholar 

  15. V. I. Bliznikas, “On the geometry of systems of first-order partial differential equations,” Tr. Geometr. Seminara, Inst. Nauchn. Inform. Akad. Nauk SSSR,2, 33–53 (1969).

    Google Scholar 

  16. V. I. Bliznikas, “On the geometry of quasilinear systems of first-order partial differential equations,” Liet. Matem. Rinkinys,9, No. 2, 205–210 (1969).

    Google Scholar 

  17. V. I. Bliznikas, “On the geometry of normal systems of higher-order partial differential equations,” Liet. Matem. Rinkinys,9, No. 2, 211–232 (1969).

    Google Scholar 

  18. V. I. Bliznikas, “On the geometry of systems of differential equations,” Liet. Matem. Rinikys,9, No. 2, 382–384 (1969).

    Google Scholar 

  19. V. V. Vagner, “On the concept of an indicatrix in the theory of partial differential equations,” Uspekhi Matem. Nauk,18, No. 2, 188–189 (1947).

    Google Scholar 

  20. V. V. Vagner, “The geometry of an n-dimensional space with an m-dimensional Riemann metric and its application to the calculus of variations,” Matem. Sb.,20(62), 3–25 (1947).

    Google Scholar 

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

    Google Scholar 

  22. A. M. Vasil'ev, “Systems of three first-order partial differential equations with three unknown functions and two independent variables (local theory),” Matem. Sb.,70, No. 4, 457–480 (1966).

    Google Scholar 

  23. V. A. Vuiichich, “Absolute integrals of differential equations of a geodesic,” Publs. Inst. Math.,12, 143–148 (1971).

    Google Scholar 

  24. V. A. Gaukhman, “Geometry of a second-order ordinary differential equation relative to a conformal transformation group of two variables,” Dokl. Akad. Nauk SSSR,140, No. 1, 15–18 (1961).

    Google Scholar 

  25. Chao-hao Ku, “On connection pairs and integral varieties of a system of second-order partial differential equations. I, II,” Acta Math. Sinica,6, No. 2, 153–169 (1956).

    Google Scholar 

  26. Chao-hao Ku “On connection pairs and integral varieties of a system of second-order partial differential equations. III,” Acta Math. Sinica,6, No. 3, 426–432 (1956).

    Google Scholar 

  27. Chao-hao Ku, “On the theory of affine imbedding,” Acta Math. Sinica,6, No. 3, 464–471 (1956).

    Google Scholar 

  28. Chao-hao Ku, “On one type of mixed equations for multidimensional spaces,” Shuxue Sinzhan,8, No. 3, 277–282 (1965).

    Google Scholar 

  29. Chao-hao Ku, “On certain differential equations of mixed type in an n-dimensional space,” Shuxue Sinzhan,8, No. 3, 277–282 (1965); translation in: Scientia Sinica,14, No. 11, 1574–1581 (1965).

    Google Scholar 

  30. L. E. Evtushik, “Structure of infinite transformation groups and the differential equations of their characteristic objects,” Repts. Second Siberian Conf. Math. Mech., 1962 [in Russian], Tomskii Univ., Tomsk (1962), pp. 79–80.

    Google Scholar 

  31. I. P. Egorov, “Motions in generalized differential-geometric spaces,” in: Progress in Mathematics, Vol. 6: Topology and Geometry (edited by R. V. Gamkrelidze), Plenum Press, New York-London (1970), pp. 171–227.

    Google Scholar 

  32. N. Kh. Ibragimov, “Classification of invariant solutions of the equations of a two-dimensional non-stationary motion of a gas,” Zh. Prikl. Mekhan. i Tekh. Fiz., No. 4, 19–22 (1966).

    Google Scholar 

  33. N. Kh. Ibragimov, Group Properties of Certain Differential Equations [in Russian], Nauka, Novosibirsk (1967), 59 pp.

    Google Scholar 

  34. N. Kh. Ibragimov, “Generalized motions in Riemann spaces,” Dokl. Akad. Nauk SSSR,178, No. 1, 27–30 (1968).

    Google Scholar 

  35. N. Kh. Ibragimov, “Groups properties of wave equations for particles with zero mass,” Dokl. Akad. Nauk SSSR,178, No. 3, 566–568 (1968).

    Google Scholar 

  36. N. Kh. Ibragimov, “Transformations preserving harmonic coordinates,” Dokl. Akad. Nauk SSSR,181, No. 5, 1050–1053 (1968).

    Google Scholar 

  37. N. Kh. Ibragimov, “On the group classification of second-order differential equations,” Dokl. Akad. Nauk SSSR,183, No. 2, 274–277 (1968).

    Google Scholar 

  38. N. Kh. Ibragimov, “On the invariance of Dirac equations,” Dokl. Akad. Nauk SSSR,185, No. 6, 1226–1228 (1969).

    Google Scholar 

  39. N. Kh. Ibragimov, “The wave equation in a Riemann space,” in: Dynamics of a Continuous Medium, No. 1 [in Russian], Nauka, Novosibirsk (1969), pp. 36–47.

    Google Scholar 

  40. N. Kh. Ibragimov, “Groups of generalized motions,” Dokl. Akad. Nauk SSSR,187, No. 1, 25–28 (1969).

    Google Scholar 

  41. N. Kh. Ibragimov, “Invariant variational problems and conservation laws (Remarks on E. Noether's theorem),” Teor. i Matem. Fiz.,1, No. 3, 350–359 (1969).

    Google Scholar 

  42. N. Kh. Ibragimov, “Conformal invariance and Huygens principle,” Dokl. Akad. Nauk SSSR,194, No. 1, 24–27 (1970).

    Google Scholar 

  43. V. L. Izrailevich, “Invariant characteristic of hypercones in the space W2,n,” Tr. Saratovsk. Inst. Mekhaniz. S. Kh., No. 26, 211–217 (1963).

    Google Scholar 

  44. V. L. Izrailevich, “Theory of cones in the space W2,n,” in: Mem. Young Scientists of Saratov Univ., Math. Issue [in Russian], Saratov (1964), pp. 37–51.

  45. V. I. Ionov, “Systems of differential equations in the theory of surfaces in the symbolism of Cartan calculus,” Tr. Mosk. Inst. Inzh. Geod. Aerofotoc” emki i Kartogr., No. 58, 55–62 (1971).

    Google Scholar 

  46. N. I. Kabanov, “Differential-geometric methods in the calculus of variations,” in: Progress in Mathematics, Vol. 12: Algebra and Geometry (edited by R. V. Gamkrelidze), Plenum Press, New York-London (1972), pp. 217–254.

    Google Scholar 

  47. É. M. Kan, “On conservation laws of quasilinear systems of four first-order partial differential equations,” Izv. Vyssh. Uchebn. Zavedenii, Matematika, No. 1, 78–80 (1968).

    Google Scholar 

  48. E. Cartan, Spaces of Affine, Projective, and Conformal Connections [Russian translation], Kazansk. Univ., Kazan' (1962), 210 pp.

    Google Scholar 

  49. Kh. O. Kil'p, “Linear invariance groups of families of planes and the corresponding G-structures,” in: Third Interinst. Sci. Conf. Prob. Geom. (Repts. Abstrs.) [in Russian], Kazan' (1967), p. 76.

  50. Kh. O. Kil'p, “Geometric structure of a family of planes given by a certain system of first-order differential equations,” Tartu Ulikooli Toimetised, No. 220, 31–42 (1968).

    Google Scholar 

  51. Kh. O. Kil'p, “On invariance groups of certain families of planes,” in: Third Baltic Geom. Conf. (Repts. Abstrs.) [in Russian], Palanga (1968), pp. 77–79.

  52. Kh. O. Kil'p, “Linear invariance groups of families of planes and the corresponding G-structures,” Tartu Ulikooli Toimetised, No. 220, 43–66 (1968).

    Google Scholar 

  53. Kh. O. Kil'p, “On the geometry of a system of three first-order partial differential equations,” Tartu Ulikooli Toimetised, No. 277, 78–97 (1971).

    Google Scholar 

  54. Kh. O. Kil'p, “Quasilinear systems of first-order partial differential equations with m unknown functions of two independent variables and with noncoinciding characteristics (geometric theory),” Tartu Ulikooli Toimetised, No. 281, 63–85 (1971).

    Google Scholar 

  55. Kh. O. Kil'p, “Quasilinear systems of first-order partial differential equations of unknown functions and two arguments with different characteristics,” in: Abstrs. Repts. Fifth All-Union Conf. Mod. Prob. Geom. [in Russian], Samarkand (1972), p. 92.

  56. G. M. Kuz'mina, “On the geometry of a system of two partial differential equations,” Uch. Zap. Mosk. Gos. Ped. Inst., No. 243, 99–108 (1965).

    Google Scholar 

  57. G. M. Kuz'mina, “Linear systems S23 1 as analogs of Dirac equations,” Izv. Vyssh. Uchebn. Zavedenii, Matematika, No. 10, 56–61 (1967).

    Google Scholar 

  58. G. M. Kuz'mina, “On the possibility of reducing a system of two first-order partial differential equations to one second-order equation,” Uch. Zap. Mosk. Gos. Ped. Inst., No. 271, 67–76 (1967).

    Google Scholar 

  59. G. M. Kuz'mina, “Functional invariant conservation laws of certain systems of quasilinear equations,” in: Third Baltic Geom., Conf. (Repts. Abstrs.) [in Russian], Palanga (1968), pp. 93–94.

  60. B. L. Laptev, “Lie differentiation,” in: Progress in Mathematics, Vol. 6: Topology and Geometry, (edited by R. V. Gamkrelidze), Plenum Press, New York-London (1970), pp. 229–269.

    Google Scholar 

  61. G. F. Laptev, “Differential geometry of immersed manifolds. Group-theoretic method of differential-geometric investigations,” Tr. Mosk. Matem. Obshch.,2, 275–382 (1953).

    Google Scholar 

  62. G. F. Laptev, “Geometric of differential equations,” in: First All-Union Geom. Conf. [in Russian], Kiev (1962), pp. 6–7.

  63. G. F. Laptev, “Manifolds immersed in generalized spaces,” in: Proc. Fourth All-Union Math. Congr., Vol. 2 [in Russian], Leningrad (1964), pp. 226–233.

    Google Scholar 

  64. G. F. Laptev, “Differential geometry of multidimensional surfaces,” in: Geometry. 1963 [in Russian], Itogi Nauki VINITI Akad. Nauk SSSR, Moscow (1965), pp. 5–64.

    Google Scholar 

  65. Ü. G. Lumiste, “Connections in homogeneous bundles,” Matem. Sb.,69, No. 3, 434–469 (1966).

    Google Scholar 

  66. Z. Yu. Lupeikis, “On the geometry of quasilinear systems of second-order differential equations,” in: Third Baltic Geom. Conf. (Repts. Abstrs.) [in Russian], Palanga (1968), pp. 107–108.

  67. Z. Yu. Lupeikis, “On the geometry of a quasilinear system of second-order differential equations,” Liet. Matem. Rinkinys,9, No. 2, 384–386 (1969).

    Google Scholar 

  68. Z. Yu. Lupeikis, “On the geometry of quasilinear systems of second-order partial differential equations,” in: Fourth All-Union Interinst. Conf. Geom. (Repts. Abstrs.) [in Russian], Tbilisi (1969), p. 71.

  69. Z. Yu. Lupeikis, “On the geometry of quasilinear systems of second-order differential equations,” Liet. Matem. Rinkinys,9, No. 3, 535–566 (1969).

    Google Scholar 

  70. Z. Yu. Lupeikis, “On the geometry of certain quasilinear systems of second-order partial differential equations,” Liet. Matem. Rinkinys,10, No. 1, 69–99 (1970).

    Google Scholar 

  71. Z. Yu. Lupeikis, “On the geometry of quasilinear systems of second-order partial differential equations,” Liet. Matem. Rinkinys,10, No. 3, 641–642 (1970).

    Google Scholar 

  72. Z. Yu. Lupeikis, “On the geometry of systems of partial differential equations,” Liet. Matem. Rinkinys,11, No. 2, 409–410 (1971).

    Google Scholar 

  73. Z. Yu. Lupeikis, “On the geometry of systems of partial differential equations,” Liet. Matem. Rinkinys,12, No. 2, 149 (1972).

    Google Scholar 

  74. Z. Yu. Lupeikis, “On the geometry of systems of first-order partial differential equations,” Liet. Matem. Rinkinys,13, No. 3, 119–139 (1973).

    Google Scholar 

  75. L. V. Ovsyannikov, “Groups and group-invariant solutions of differential equations,” Dokl. Akad. Nauk SSSR,118, No. 3, 439–442 (1958).

    Google Scholar 

  76. L. V. Ovsyannikov, “A new solution of the equations of hydrodynamics,” Dokl. Akad. Nauk SSSR,123, No. 2, 262–265 (1958).

    Google Scholar 

  77. L. V. Ovsyannikov, “Group properties on the nonlinear heat-conductivity equation,” Dokl. Akad. Nauk SSSR,125, No. 3, 492–495 (1959).

    Google Scholar 

  78. L. V. Ovsyannikov, “On the search for the group of a linear second-order differential equation,” Dokl. Akad. Nauk SSSR,132, No. 1, 44–47 (1960).

    Google Scholar 

  79. L. V. Ovsyannikov, Group Properties of Differential Equations [in Russian], Izd. Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk (1962), 239 pp.

    Google Scholar 

  80. L. V. Ovsyannikov, “On infinite groups of mappings given by differential equations,” Dokl. Akad. Nauk SSSR,148, No. 1, 36–39 (1963).

    Google Scholar 

  81. L. V. Ovsyannikov, “Lie groups and partial differential equations,” Proc. Fourth All-Union Math. Congr., 1961, Vol. 2 [in Russian], Nauka, Leningrad (1964), p. 531.

    Google Scholar 

  82. L. V. Ovsyannikov, “Group-invariant solutions of the equations of hydrodynamics,” Proc. Second All-Union Congr. Theoret. Appl. Mech., 1964, Survey of Reports, Part 2 [in Russian], Nauka, Moscow (1965), pp. 302–305.

    Google Scholar 

  83. L. V. Ovsyannikov, “On one class of nonsteady-state motions of an incompressible fluid,” Proc. Fifth Session Sci. Council National-Econ. Util. Detonation [in Russian], Frunze (1965), pp. 34–42.

  84. L. V. Ovsyannikov, Lectures on the Theory of Group Properties of Differential Equations [in Russian], Novosibirsk (1966), 131 pp.

  85. L. V. Ovsyannikov, “Partial invariance,” Dokl. Akad. Nauk SSSR,186, No. 1, 22–25 (1969).

    Google Scholar 

  86. L. V. Ovsyannikov, “Group bundle of boundary-layer equations,” in: Dynamics of a Continuous Medium, No. 1 [in Russian], Nauka, Novosibirsk (1969), pp. 24–35.

    Google Scholar 

  87. L. V. Ovsyannikov, “Group properties of the equations of mechanics,” in: Mechanics of a Continuous Medium and Related Problems of Analysis [in Russian], Nauka, Moscow (1972), pp. 381–393.

    Google Scholar 

  88. L. N. Orlova, “System of two partial differential equations of first and second order with two functions of two independent variables,” Uch. Zap. Mosk. Gos. Ped. Inst.,271, No. 7, 103–112 (1967).

    Google Scholar 

  89. A. Z. Petrov, “Geometry and physical space-time,” in: Algebra. Topology. Geometry. 1966 [in Russian], Itogi Nauki VTNITI Akad. Nauk SSSR, Moscow (1968), pp. 221–265.

    Google Scholar 

  90. D. K. Petrushkevichyute, “Special groups admissible by quasilinear systems S (1)3,2 ” in: Repts. Abstrs. Fifth All-Union Conf. Mod. Prob. Geom. [in Russian], Samarkand (1972), p. 166.

  91. V. A. Podol'skii, “On systems with common trajectories,” Tr. Vses. Zaochn. Energ. Inst., No. 33, 72–77 (1967).

    Google Scholar 

  92. V. A. Podol'skii “Moving systems of trajectories,” Tr. Mosk. Inst. Radiotekhn. Élektr. i Avtomatiki, No. 46, 97–99 (1970).

    Google Scholar 

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

    Google Scholar 

  94. D. M. Sintsov, Papers on Nonholonomic Geometry [in Russian], Vishcha Shkola, (1972), 296 pp.

  95. N. V. Stepanov, “Invariants of two two-parameter families of curves on a plane (Abstract),” Uch. Zap. Velikoluksk. Gos. Ped. Inst., No. 12, 64 (1960).

    Google Scholar 

  96. N. V. Stepanov, “The Laplace transform in a space of straight lines,” Izv. Vyssh. Uchebn. Zavedenii, Matematika, No. 3, 127–135 (1961).

    Google Scholar 

  97. N. V. Stepanov, “Geometry of two second-order ordinary differential equations,” Dokl. Akad. Nauk SSSR,140, No. 1, 62–65 (1961).

    Google Scholar 

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

    Google Scholar 

  99. N. V. Stepanov, “On the geometry of one class of equations y″ ′=f(x, y, y′, y″),” Uspekhi Matem. Nauk,21, No. 3, 237–238 (1966).

    Google Scholar 

  100. N. V. Stepanov, “On pairs of ordinary differential equations, admitting of a finite transitive Lie group,” Uch. Zap. Pskovsk. Ped. Inst., No. 31, 5–8 (1966).

    Google Scholar 

  101. N. V. Stepanov, “Local equivalence of second-order ordinary differential equations,” in: Third Baltic Geom. Conf. (Repts. Abstrs.) [in Russian], Palanga (1968), pp. 152–154.

  102. N. V. Stepanov, “Joint invariants of two families of curves on a plane,” Tr. Geometr. Seminara, Inst. Nauchn. Inform. Akad. Nauk SSSR,2, 299–331 (1969).

    Google Scholar 

  103. N. V. Stepanol, “Fundamental properties of E-groups on a plane,” Izv. Vyssh. Uchebn. Zavedenii, Matematika, No. 7, 71–80 (1971).

    Google Scholar 

  104. N. V. Stepanov, “A family of curves invariantly associated with the equation y(n)=f(x, y, y1,..., y(n−1))” in: Repts. Abstrs. Fifth All-Union Conf. Mod. Prob. Geom. [in Russian], Samarkand (1972), p. 208.

  105. A. S. Udalov, “On the theory of curves in a projective space of n dimensions,” Dokl. Akad. Nauk SSSR,146, No. 1, 46–49 (1962).

    Google Scholar 

  106. A. S. Udalov, “Theory of curves and its application to linear differential equations,” Matem. Sb.,61, No. 4, 426–442 (1963).

    Google Scholar 

  107. A. S. Udalov, “On certain classes of curves in Pn and linear differential equations,” in: Repts. Abstrs. Fifth All-Union Conf. Mod. Prob. Geom. [in Russian], Samarkand (1972), p. 220.

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

    Google Scholar 

  109. A. P. Shirokov, “Structure on differentiable manifolds,” in: Progress in Mathematics, Vol. 9: Algebra and Geometry (edited by R. V. Gamkrelidzé), Plenum Press, New York-London (1971), pp. 137–207.

    Google Scholar 

  110. A. Aeppli, “On the uniqueness of compact solutions for certain elliptic differential equations, Proc. Amer. Math. Soc.,11, No. 5, 826–832 (1960).

    Google Scholar 

  111. L. Auslander, “An ideal theory for exterior differential equations,” Ann. Math.,63, No. 3, 527–534 (1956).

    Google Scholar 

  112. L. Auslander and L. Markus, “Classical differential equations on manifolds,” Trans. Amer. Math. Soc.,91, No. 1, 113–128 (1959).

    Google Scholar 

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

    Google Scholar 

  114. L. Berwald, “Über Systeme von gewöhnlichen Differentialgleichungen zweiter Ordnung, der Integralkurven mit dem System der Geraden Linien topologisch aquivalent sind,” Ann. Math.,48, No. 2, 193–215 (1947).

    Google Scholar 

  115. L. Bieberbach, “Tschebyshefnetze auf RotationSciflächen,” Ann. Mat. Pura ed Appl.,55, 173–295 (1961).

    Google Scholar 

  116. E. Bompiani, “Geometria degli elementi differenziali,” in: Leonhard Euler 250. Geburgstag, Akad. Verlag, Berlin (1959), pp. 49–77.

    Google Scholar 

  117. E. Bompiani, “Sulla geometria dell'equazione differenziale: y″ ′=G(x, y, y′)y″+H (x, y, y)y″2,” Atti. Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. e Natur.,46, No. 5, 535–540 (1969).

    Google Scholar 

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

    Google Scholar 

  119. M. Breuer, Jacobische Differentialgeometrie und Systeme partieller Differentialgleichungen 1. Ordnung, Bonn Math. Schr., No. 7, Bonn (1958), 74 S.

  120. C. Carathéodory, “Über die diskontinuierlichen Lösungen in der Variationsrechung,” Dissertation, Göttingen (1904), 71 pp.

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

    Google Scholar 

  122. S. Chern, “Sur la géométrie d'une équation différentielle du troisième ordre,” C. R. Acad. Sci. Paris,204, 1227–1229 (1937).

    Google Scholar 

  123. S. Chern, “The geometry of the differential equation y″ ′=F(x, y, y′, y″),” Sci. Rep. Nat. Tsing Hua Univ., (A),4, 97–111 (1940).

    Google Scholar 

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

    Google Scholar 

  125. H. V. Craig, “On tensor relative of the extended point transformation,” Amer. J. Math.,59, 764–774 (1937).

    Google Scholar 

  126. H. V. Criag, “On extensors and a Euclidean basis for higher order spaces,” Amer. J. Math.,61, 791–808 (1939).

    Google Scholar 

  127. H. V. Criag, Vector and Tensor Analysis, McGraw-Hill Book Co. Inc., New York (1943).

    Google Scholar 

  128. H. V. Craig, “On the multiple parameter Jacobian extensor,” Tensor (NS), 27–35 (1952).

  129. H. V. Criag, “On certain linear extensor equations,” Tensor,4, No. 1, 40–50 (1954).

    Google Scholar 

  130. H. V. Craig, “On certain linear extensor equations. Paper II,” Tensor,5, No. 2, 77–84 (1955).

    Google Scholar 

  131. H. V. Craig, “On extensors, first order partial differential equations and Poisson brackets,” Tensor,6, No. 3, 159–164 (1956).

    Google Scholar 

  132. P. Dedecker, “Systèmes différentiels extérieurs, invariants integraux et suites spectrales,” Convegno Internazionale di Geometria Differenziale, Italia, 1953, Ed. Cremonese, Roma (1954), pp. 247–262.

  133. D. C. Demaria, “I sistemi ∞6 di curve spaziali godenti della proprietà conforme in prima approssimazione,” Rend. Semin. Mat. Univ. Politecn. Torino,13, 251–262 (1953–1954).

    Google Scholar 

  134. A. Dobrescu, “Asupra grupurilor de miscari ale ecuatiilor cu derivate partiale de ordinul al doilea, în două variabile,” Studi si Cerc. Mat. Acad. RPR,11, No. 2, 505–520 (1960).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  137. V. Dumitras, “Sur le groupe de stabilité d'un espace Hn,” Bull. Math. Soc., Sci. Math. et Phys., RPR,3, No. 1, 17–20 (1959).

    Google Scholar 

  138. C. Ehresmann, “Les prolongements d'une variété différéntiable. I. Calculus des jets prolongement, principal,” C. R. Acad. Sci. Paris,233, 598–600 (1951).

    Google Scholar 

  139. C. Ehresmann, “Les prolongements d'une variété différentiable. II. L'espace des jets d'ordre r de Vn dans Vm,” C. R. Acad. Sci. Paris,233, 777–779 (1951).

    Google Scholar 

  140. C. Ehresmann, “Les prolongements d'une variété différentiable. III. Transitivité des prolongements,” C. R. Acad. Sci. Paris,233, 1081–1083 (1951).

    Google Scholar 

  141. C. Ehresmann, “Les prolongements d'une variété différentiable,” Atti IV Congresso Unione Mat. Italiana, Taormina Ott. (1951), pp. 1–9.

  142. C. Ehresmann, “Structures locales et structures infinitésimales,” C. R. Acad. Sci. Paris,234, 587–589 (1952).

    Google Scholar 

  143. C. Ehresmann, “Les prolongements d'une variété différentiable. IV. Éléments de contact et éléments d'enveloppé,” C. R. Acad. Sci. Paris,234, 1028–1030 (1952).

    Google Scholar 

  144. C. Ehresmann, “Les prolongements d'une variété différentiable. V. Covariants différentiels et prolongements d'une structure infinitésimale,” C. R. Acad. Sci. Paris,234, 1424–1425 (1952).

    Google Scholar 

  145. R. B. Gardner, Differential geometric methods in partial differential equations,” Doct. Diss. Univ. Calif., Berkeley (1965), 158 pp; Dissert. Abstrs.,26, No. 7, 3976 (1966).

    Google Scholar 

  146. H. Goldschmidt, “Existence theorems for analytic linear partial differential equations,” Ann. Math., Ser. 2,86, No. 2, 246–270 (1967).

    Google Scholar 

  147. H. Goldschmidt, “Integrability criteria for systems of nonlinear partial differential equations,” J. Different. Geom.,1, No. 3, 269–307 (1967).

    Google Scholar 

  148. H. Goldschmidt, “Prolongations of linear partial differential equations. I. A conjecture of E. Cartan,” Ann. Sci. École Norm. Supér.,1, No. 2, 417–444 (1968).

    Google Scholar 

  149. H. Goldschmidt, “Prolongations of linear partial differential equations. II. Inhomogeneous equations,” Ann. Sci. École Norm. Supér.,1, No. 4, 617–625 (1968).

    Google Scholar 

  150. H. Goldschmidt, “Sur la structure des équations de Lie,” J. Different. Geom.,6, No. 3, 357–373 (1972).

    Google Scholar 

  151. V. Guillemin, “Some algebriac results concerning the characteristics of overdetermined system of partial differential equations,” Amer. J. Math.,90, No. 1, 270–284 (1968).

    Google Scholar 

  152. V. Guillemin and M. Kuranishi, “Some algebraic results concerning involutive subspaces,” Amer. J. Math.,90, No. 4, 1307–1320 (1968).

    Google Scholar 

  153. A. Haimovici, “Geometria unei ecuatii Monge de tip particular,” Studi si Cerc. Stiint.,5, Nos. 1–2, 17–27 (1954).

    Google Scholar 

  154. A. Haimovici, “Asupra echivalentei a doua spatii cu conexiune afină,” Studi si Cerc. Stiint.,10, No. 1, 95–106 (1959).

    Google Scholar 

  155. A. Haimovici, “Espaces à connexion affine tridimensionnels qui admettent la notion d'aire,” Pubis. Math.,7, Nos. 1–4, 211–225 (1960).

    Google Scholar 

  156. A. Haimovici, “Sur une interpretation géométrique des systèmes de Pfaff completement intégrables et sur leur arbitrariete,” An. Stiint. Univ. Iasi, Sec. la,11b, 239–250 (1965).

    Google Scholar 

  157. A. Haimovici, “Courbure et torsion des espaces á connexion non-linéaire. Espaces à courbure donnée,” An. Stiint. Univ. Iasi, Sec. 1a,12, No. 1, 127–137 (1966).

    Google Scholar 

  158. M. Haimovici, “Despre prelungarea ecuatiilor de ord II cu functio necunoscuta de doua variabile indspendente si despre transformările acestor ecuatti,” An. Stiint. Univ., Sec. I,1, Nos. 1–2, 69–136 (1955).

    Google Scholar 

  159. M. Haimovici, “Sulla decomposizione del prolungamento di un sistema differenziale,” Atti. Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. e Natur.,25, Nos. 3–4, 152–159 (1958).

    Google Scholar 

  160. M. Haimovici, “Sur la décomposition des systèmes différentiels extérieurs,” Abstr. Short Communs. Internat. Congr. Math. in Edinburg, Univ. Edinburgh (1958), pp. 113–114.

  161. T. Hangan, “Ecuatii cu derivate partiale satisfăcute de transformările grupuli projectiv si conform,” An. Univ. “C. I. Parhon,” Ser. Stiint. Natur., No. 19, 33–37 (1958).

    Google Scholar 

  162. T. Hangan, “Pseudogrupul projectiv grassmannian,” An. Stiint. Univ. Iasi, Sec. 1a,11b, 349–356 (1965).

    Google Scholar 

  163. B. K. Harrison and F. B. Estabrook, “Geometric approach to invariance groups and solution of partial differential systems,” J. Math. Phys.,12, No. 4, 653–666 (1971).

    Google Scholar 

  164. H. Hashimoto, “On the geometry of a system of partial differential equations of third order,” J. Fac. Sci. Hokkaido Univ., Ser. Math.,8, No. 4, 163–172 (1940).

    Google Scholar 

  165. I. Hayashi, “On the characters of the prolonged differential system,” Nagoya Math. J.,28, 63–68 (1966).

    Google Scholar 

  166. R. E. Hermann, “Cartan's geometric theory of partial differential equations,” Adv. Math.,1. No. 3, 265–317 (1965).

    Google Scholar 

  167. S. Hokari, “Über die Bivektorübertragung,” J. Fac. Sci. Hokkaido Univ.,11, 103–117 (1934).

    Google Scholar 

  168. S. Hokari, “Über die Geometrie des systems der partiellen Differentialgleichungen dritter Ordnung,” Proc. Acad. Tokyo,16, No. 7, 104–108 (1940).

    Google Scholar 

  169. S. Hokari, “Die intrinsice Theorie der Geometrie des Systems der partiellen Differentialgleichungen,” Proc. Acad. Tokyo,16, No. 8, 326–332 (1940).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  172. F. A. Homann, “On transformations preserving Laguerre-Forsyth canonical form,” Proc. Amer. Math. Soc.,9, No. 3, 408–411 (1958).

    Google Scholar 

  173. H. Hombu, “Zur Theories der Affinorübertragung,” Proc. Acad. Tokyo,12, No. 5, 109–111 (1936).

    Google Scholar 

  174. H. Hombu, “Projektive Transformation eines Systems der gewöhnlichen Differentialgleichungen dritter Ordnung,” Proc. Acad. Tokyo,13, 187–190 (1937).

    Google Scholar 

  175. H. Hombu, “Projektiven Parameter der verallgemeinerten ‘paths’,” Proc. Acad. Tokyo,13, 406–409 (1937).

    Google Scholar 

  176. H. Hombu, “Die projektive Theories der ‘paths’,” Proc. Acad. Tokyo,13, 410–413 (1937).

    Google Scholar 

  177. Hou-Sung Hu, “A new geometry of a space of K-spreads,” Sci. Rec.,3, No. 3, 107–111 (1959).

    Google Scholar 

  178. Xuan-je Hua, “Positively flat spaces and subprojectively flat spaces of K-spreads,” Sci. Abstrs. China Math. and Phys. Sci.,3, No. 1, 2 (1965).

    Google Scholar 

  179. R. L. Ingraham, “The geometry of the second linear partial differential equation of the second order,” Amer. J. Math.,75, No. 4, 691–698 (1953).

    Google Scholar 

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

    Google Scholar 

  181. H. H. Johnson, “Partial prolongations and the characteristics of differential equations,” Trans. Amer. Math. Soc.,146, 231–240 (1969).

    Google Scholar 

  182. M. Jurchescu, “Recouvrements riemanniens définis par des equations différentielles du second ordre,” C. R. Acad. Sci. Paris,245, No. 6, 627–630 (1957).

    Google Scholar 

  183. A. Kaiser, Inaugural Dissertation, Teubner, Leipzig (1913).

    Google Scholar 

  184. G. H. Katzin and J. Levine, “Note on the equations of projective collineations,” Tensor,19, No. 2, 162–164 (1968).

    Google Scholar 

  185. A. Kawaguchi and H. Hombu, “Die Geometrie des Systems der partiellen Differentialgleichungen,” J. Fac. Sci. Hokkaido Univ., Ser. 1,6, No. 1, 21–62 (1936).

    Google Scholar 

  186. A. Kawaguchi, “On the contractions of extensors,” Proc. Acad. Tokyo,14, 237–241 (1938).

    Google Scholar 

  187. A. Kawaguchi, “Einige Sätze über die Extensoren,” Ann. Soc. Polonaise de Math.,17, 166–176 (1938).

    Google Scholar 

  188. A. Kawaguchi, “Eine Verallgemeinerung von Extensoren,” Monatsch. Math. Phys.,48, 329–339 (1939).

    Google Scholar 

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

    Google Scholar 

  190. T. Klemona, “Über lineare partielle Differentialgleichungen erster Ordnung,” Suomalais Tiedeakat. Toimituks, Ser. A1, No. 260, 1–26 (1958).

    Google Scholar 

  191. K. Kodaira, “On deformations of some complex pseudogroup structures,” Ann. Math.,71, No. 2, 224–302 (1960).

    Google Scholar 

  192. K. Kodaira and D. C. Spencer, Multifoliate structures,” Ann. Math.,74, No. 1, 52–100 (1961).

    Google Scholar 

  193. A. Koppisch, “Zur Invariantentheorie der gewöhnlichen Differentialgleichungen zweiter Ordnung,” Inaugural Dissertation, Teubner, Leipzig (1905).

    Google Scholar 

  194. D. D. Kosambi, “Parallelste and path-space,” Math. Z.,37, 608–618 (1933).

    Google Scholar 

  195. D. D. Kosambi, “Path-spaces of higher order,” Quart. J. Math.,7, 97–105 (1936).

    Google Scholar 

  196. D. D. Kosambi, “Lie rings in path-space,” Proc. Nat. Acad. Sci. USA,35, 389–394 (1949).

    Google Scholar 

  197. A. Kriszten, “Zur Geometrie der partiellen Differentialgleichungen 2. Ordnung,” Math. Ann.,158, No. 1, 35–45 (1965).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  200. Chao-hao Ku, “Differentiable solutions of positive symmetric partial differential equations,” Acta Math. Sinica,14, No. 4, 503–516 (1964).

    Google Scholar 

  201. A. Kumpera, “Sur l'intégration d'une classe remarquable des systémes différentiels automorphes par la méthode de Sophús Lie,” Cahiers Topol. et Géom. Différent. Ch. Ehresmann, Fac. Sci. Paris,9, No. 3, 255–280 (1967).

    Google Scholar 

  202. M. Kuranishi, “On E. Cartan's prolongation theorem of exterior differential systems,” Amer. J. Math.,79, No. 1, 1–47 (1957).

    Google Scholar 

  203. M. Kuranishi, Lectures on Exterior Differential Systems, Tata Inst. of Fundamental Research, Bombay (1962).

    Google Scholar 

  204. M. Kuranishi, “Sheaves defined by differential equations and application to deformation theory of pseudo-group structures,” Amer. J. Math.,86, No. 2, 379–381 (1964).

    Google Scholar 

  205. M. Kuranishi, Lectures on Involutive Systems of Partial Differential Equations, Pubis. Soc. Mat. Sao Paulo, Sao Paulo (1967), 77 pp.

    Google Scholar 

  206. S. Lie, Vorlesungen über Differentialgleichungen mit bekannten Infinitesimalen Transformationen, Bearbeitet und hrs von Geor Scheffers, Teubner, Leipzig (1891), 568 pp.

    Google Scholar 

  207. S. Lie, Gesammelte Abhandlungen wia Tebner-Aschehong & Co., 1924, Bd. 4. Abhandlungen zur Theorie der Differentialgleichungen 2-te Abt., 1929, Bd. 4, Anmerkung zum 4-ten Band, (1929), 235 S.

  208. R. Lelienthal, Grundlagen der Krümmungslehre der Kurvenschaaren (1896), 114 pp.

  209. R. Lilienthal, “Über die krümmung der Kurvenschaaren,” Math. Ann.,B32, 545–565 (1931).

    Google Scholar 

  210. M. Matsumoto, “Paths in a Finsler space,” J. Math. Kyoto Univ.,3, No. 3, 305–318 (1964).

    Google Scholar 

  211. Y. Matsushima, “On a theorem concerning the prolongation of a differential system,” Nagoya Math. J.,6, 1–16 (1953).

    Google Scholar 

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

    Google Scholar 

  213. R. Mirodan, “Geometrizarea ecuatiilor cu derivate partiale liniare si omogene,” An. Univ. “C. J. Parhon,” Ser. Stiint. Natur., No. 14, 35–39 (1957).

    Google Scholar 

  214. A. Moór, “Über projektive Veränderung der Übertragung in Linienelementmannigfaltigkeiten,” Acta Sci. Math.,24, Nos. 1–2, 119–128 (1963).

    Google Scholar 

  215. A. Moór, “Über spezielle Bahnengeometrien dritter Ordnung,” Ann. Pol. Math.,17, No. 3, 261–271 (1966).

    Google Scholar 

  216. A. Myller, “Drumuri de profil longitudinal dat,” Stud. si Cerc. Stiint,4, Nos. 1–2, 1–17 (1953).

    Google Scholar 

  217. F. Neuman, “Centroaffine invariants of plane curves in connection with the theory of the second-order linear differential equations,” Arch. Math.,4, No. 4, 201–216 (1968).

    Google Scholar 

  218. M. Obata, “Riemannian manifolds admitting a solution of a certain system of differential equations,” Proc. U. S.-Japan Semin. Different. Geom., Kyoto, 1965, Nippon Hycronsha Co., Ltd. Tokyo (1966), pp. 101–114.

    Google Scholar 

  219. T. Ohkubo, “Die Geometrie der partiellen Differentialgleichungen dritter Ordnung,” J. Fac. Sci. Hokkaido Univ., Ser. 1,6, No. 1, 113–124 (1937).

    Google Scholar 

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

    Google Scholar 

  221. W. Oliva, “Sur quelques conditions d'intégrabilité pour certains systèmes d'équations aux derivées partielles,” C. R. Acad. Sci. Paris,261, No. 17, 3275–3278 (1965).

    Google Scholar 

  222. M. Prvanovitch, “Hyper-Darboux lines on a surface in three-dimensional Euclidean space,” Bull. Calcutta Math. Soc.,47, No. 1, 55–60 (1955).

    Google Scholar 

  223. P. Quillen, “Formal properties of overdetermined systems of linear partial differential equations,” Thesis, Harvard Univ., Cambridge, Mass. (1964).

    Google Scholar 

  224. H. E. Rauch, “Geodesies and Jacobi equations on homogeneous riemannian manifolds,” Proc, U.S.Japan Semin. Different. Geom., Kyoto, 1965, Nippon Hycronsha Co., Ltd. Tokyo (1966), pp. 115–127.

    Google Scholar 

  225. S. Ruscior, “Sur un système d'équations différentialles issues du problème de la correspondance par parallélisme en E5,” Bul. Inst. Politehn. Iasi,16, Nos. 1–2, 1/9–1/11 (1970).

    Google Scholar 

  226. R. M. F. Sauer, “Projektiv geometrische Sätze über lineare partielle Differentialgleichungen 2. Ordnung,” Proc. Int. Congr. Math., Vol. 2, 1954, Amsterdam (1954), pp. 252–253.

    Google Scholar 

  227. B. Segre, “Differentiable varieties imbedded in projective space and homogeneous systems of linear partial differential equations,” Tensor,13, 101–110 (1963).

    Google Scholar 

  228. W. Slebodzinski, “Sur les équations canoniques de Hamilton,” Bull. Cl. Sci. Acad. Roy. Belg., Ser. 5,17, No. 6, 864–870 (1931).

    Google Scholar 

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

    Google Scholar 

  230. W. Slebdozinski, “Sur deux groupes infinis et continus,” Zastosow. Mat.,10, 17–30 (1969).

    Google Scholar 

  231. D. C. Spencer, “Deformation of structures on manifolds defined by transitive continuous pseudogroups. Part. I. Infinitesimal deformations of structures,” Ann. Math.,76, No. 2, 306–398 (1962).

    Google Scholar 

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

    Google Scholar 

  233. Bu-chin Su, “On the isomorphiic transformations of K-spreads in a Douglas space. II,” Acad. Sinica Sci. Record,2, 139–146 (1948).

    Google Scholar 

  234. Bu-chin Su, “A characteristic property of affine collineations in a space of K-spreads,” Bull. Amer. Math. Soc.,54, 136–138 (1948).

    Google Scholar 

  235. Bu-chin Su, “Axiom of the plane in a space of K-spreads,” Acad. Sinica Sci. Records3, 7–16 (1950).

    Google Scholar 

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

    Google Scholar 

  237. Bu-chin Su, “Axiom of the plane in a descriptive geometry of K-spreads,” Math. Nachr.,16, Nos. 3–4, 215–226 (1957).

    Google Scholar 

  238. Bu-chin Su, “A generalization of descriptive collineations in a space of K-spreads,” Math. Nachr.,16, Nos. 3–4, 227–232 (1957).

    Google Scholar 

  239. Bu-chin Su, “Recent progress in the differential geometry of a space of K-spreads,” Lucrările Consf. Geometrie si Topol., 1958, Acad. RPR, Bucuresti (1962), pp. 21–30.

    Google Scholar 

  240. Bu-chin Su and Chao-hao Ku, “The developments of differential geometry in China for the past ten years,” Sci. Sinica,8, No. 11, 1238–1242 (1959).

    Google Scholar 

  241. T. Suguri, “The geometry of K-spreads of higher order,” Mem. Fac. Sci. Kyushu Univ., Ser. A,1, No. 2, 143–166 (1941).

    Google Scholar 

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

    Google Scholar 

  243. A. Švec, “Submanifolds of Klein spaces,” Czech. Math. J.,19, No. 3, 492–499 (1969).

    Google Scholar 

  244. K. Takano, “On a representation of general affine paths,” Tensor,4, No. 3, 129–134 (1955).

    Google Scholar 

  245. L. Tamassy, “Über die geometrische Anwendung eines Differentialgleichungssystems,” Acta Math. Acad. Sci. Hung.,11, Nos. 1–2, 187–195 (1960).

    Google Scholar 

  246. M. Tarina and C. Artin, “Observatii privind clasificarea spatiilor Pn cu conexiune proiectivă fără torsiune,” Studi si Cerc. Mat. Acad. RSR,22, No. 1, 109–116 (1970).

    Google Scholar 

  247. J. D. Teodorescu and J. Rusu, “Asupra spatiilor bidimensionale cu conexiune afină local euclidiană si transformăble cremoniene întregi,” An. Univ. Bucuresti, Ser. Stiint, Natur.,10, No. 29, 199–208 (1961).

    Google Scholar 

  248. J. M. Thomas, “Conformal invariants,” Proc. Nat. Acad. USA,12, 389–393 (1925).

    Google Scholar 

  249. T. Y. Thomas, “On the projective and equi-projective geometries of paths,” Proc. Nat. Acad. Sci. USA,11, No. 4, 199–203 (1925).

    Google Scholar 

  250. T. Y. Thomas, “Systems of total differential equations defined over simply connected domains,” Ann. Math., Ser. 2,35, No. 4, 730–734 (1934).

    Google Scholar 

  251. 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, No. 2, 67–77 (1954).

    Google Scholar 

  252. M. A. Tresse, “Détermination des invariants ponctuels de l'equation différentielle ordinaire du ordre second,” Leipzig (1896).

  253. G. Tsangas, “Sur deux classes particulieres de congruences de normales,” C. R. Acad. Sci. Paris,263, No. 13, A407-A409 (1966).

    Google Scholar 

  254. M. Uchiyama, “A theory of differential equations viewed through group parameter extensions, I. A global theory of a system of total differential equations,” Yokohama Math. J.,7, No. 1, 43–56 (1959).

    Google Scholar 

  255. J. Vala, “Doppelverhältnisscharen mit zusammenfallenden oder imaginären Grundkurven auf Regelflachen,” Mat.-Fyz. Casop.,16, No. 4, 337–348 (1966).

    Google Scholar 

  256. O. Varga, “Verallgemeinerte Riemannsche Normalkoordinaten und einige Anwendungen derselben,” Izv. Mat. Inst. Blg. Akad. Nauk,4, 61–71 (1959).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  259. O. Veblen, “Generalized protective geometry,” J. London Math. Soc.,4, 140–160 (1929).

    Google Scholar 

  260. O. Veblen, A. Taub, and J. Neumann, “The Dirac equation in projective relativity,” Proc. Nat. Acad. Sci. USA, 20, No. 6 (1934).

    Google Scholar 

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

    Google Scholar 

  262. O. Veblen and T. Y. Thomas, “Projective coordinates for the geometry of paths,” Proc. Nat. Acad. Sci. USA,11, 204–207 (1925).

    Google Scholar 

  263. O. Veblen and T. Y. Thomas, “Projective invariants of affine geometry of paths,” Ann. Math.,27, 178–196 (1926).

    Google Scholar 

  264. P. Vincensini, “Sur certaines équations aux dérivées partielles du deuxième ordre,” Ann. Sci. École Norm. Supér.,75, No. 2, 153–166 (1958).

    Google Scholar 

  265. A. Voss, “Geometrische Interpretation der Differentialgleichungen Pdx+Qdy+Rdz=0,” Math. Ann.,B16, 556–559 (1924).

    Google Scholar 

  266. A. Voss, “Zur Theorie der Allgemeinen Punkt-Ebenen-Systeme,” Math. Ann.,B23, 45–81 (1926).

    Google Scholar 

  267. Gh. Vranceanu, “Sur les espaces à connexion projective,” C. R. Acad. Sci. Paris,242, No. 1, 61–63 (1956).

    Google Scholar 

  268. Gh. Vranceanu, Vorlesungen über Differentialgeometrie. Teil II, Acad.-Verlag, Berlin (1961), 405 pp.

    Google Scholar 

  269. Gh. Vranceanu, Opera Matematică. Vol. I, Acad. RSR, Bucuresti (1969), 545 pp.

    Google Scholar 

  270. V. Vagner [Wagner], Geometria del Calcolo delle Variazioni. Vol. II, Centro Internationale Matematico Estivo (CEME), Gremonese, Roma (1965), 172 pp.

    Google Scholar 

  271. K. Weise, “Der berührungstensor zweier Flächen und die Affinogeometrie der Tp im Am. I, II,” Math. Z.,43, 469–480 (1938).

    Google Scholar 

  272. T. Weszely and M. Szilágyi, “O interpretare diferential geometrica a curbelor integrale ale unui sistem de ecuatii diferentiale de ordinul doi,” Studi si Cerc. Mat. Acad. RSR, 19, No. 2, 273–280 (1967).

    Google Scholar 

  273. A. Winternitz, “Über die affine Grundlage der Metrik eines Variationsproblems,” S.-B. Preuss. Akad. Wiss.,26, 457–469 (1930).

    Google Scholar 

  274. K. Yano and H. Hiramatsu, “On projective geometry of K-spreàds,” Compos. Math.,10, 286–296 (1952).

    Google Scholar 

  275. K. Yano and H. Hiramatsu, “On groups of projective collineations in a space of K-spreads,” J. Math. Soc. Jap.,6, No. 2, 131–150 (1954).

    Google Scholar 

  276. Chin-Ta Yen, “Sur la connection projective normale associée à un feuilletage du deuxiéme ordre,” Ann. Mat. Pura ed Appl., Ser. 4,34, 55–94 (1953).

    Google Scholar 

  277. K. Yosida, “On the asymptotic property of the differential equation y″+H(x)y=f(x, y, y′),” Japan J. Math.,9, 145–159 (1932).

    Google Scholar 

  278. K. Zorawski, “Über gewisse Differentialinvarianten der Systeme gewöhnlicher Differentialgleichungen zweiter Ordnung,” Bull. Int., Acad. de Boheme (1915).

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Translated from Itogi Nauki i Tekhniki (Algebra. Topologiya. Geometriya), Vol. 11, pp. 209–259.

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Bliznikas, V.I., Lupeikis, Z.Y. Geometry of differential equations. J Math Sci 4, 591–623 (1975). https://doi.org/10.1007/BF01084051

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