Journal of Mathematical Sciences

, Volume 204, Issue 6, pp 742–759 | Cite as

Polynumbers, Norms, Metrics, and Polyingles



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  1. 1.
    M. Anastasiei and R. Miron, “Preface for generalized Finsler metrics,” in: Finsler Geom.: J. Summer Res. Conf., Seattle, Wash., July 16–20, 1995, Providence, Rhode Island (1996), pp. 157–159.Google Scholar
  2. 2.
    A. K. Aringazin and G. S. Asanov, “Problems of finslerian theory of gauge fields and gravitation,” Repts. Math. Phys. Warsz., 25, 183–241 (1988).CrossRefMATHGoogle Scholar
  3. 3.
    E. F. Beckenbach and R. Bellman, Inequalities, Springer-Verlag, Berlin–Göttingen–Heidelberg (1961).CrossRefGoogle Scholar
  4. 4.
    T. Q. Binh, “Cartan-type connections and connection sequences,” Publ. Math., 35, Nos. 3–4, 221–229 (1985).MathSciNetGoogle Scholar
  5. 5.
    P. M. Cohn, Universal Algebra, Reidel, Dordrecht, Netherlands (1981).CrossRefMATHGoogle Scholar
  6. 6.
    A. Grey and L. M. Hervella, “The sixteen classes of almost Hermitian manifolds and their linear invariants,” Ann. Math. Pure Appl., 123, No. 4, 35–58 (1980).CrossRefGoogle Scholar
  7. 7.
    G. H. Hardy, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, Am. Math. Soc., Providence, Rhode Island (1999).Google Scholar
  8. 8.
    M. Hashiguchi, “On generalized Finsler spaces,” An. Sti. Univ. Iasi. Sec. 1a, 30, No. 1, 69–73 (1984).MATHMathSciNetGoogle Scholar
  9. 9.
    M. Hashiguchi, “Some topics on Finsler geometry,” Conf. Sem. Mat. Univ. Bari., 210 (1986).Google Scholar
  10. 10.
    S. Ikeda, “On the Finslerian metrical structures of the gravitational field,” An. Sti. Univ. Iasi. Sec. 1a, 30, No. 4, 35–38 (1984).MATHGoogle Scholar
  11. 11.
    S. Ikeda, “Theory of fields in Finsler spaces,” Sem. Mec. Univ. Timisoara, No. 8, 1–43 (1988).Google Scholar
  12. 12.
    S. Ikeda, “On the theory of gravitational field in Finsler spaces, Tensor, 50, No. 3, 256–262 (1991).MATHMathSciNetGoogle Scholar
  13. 13.
    A. A. Ketsaris, Algebraic Foundations of Physics. Space-Time and Action as Universal Algebras [in Russian], Editorial URSS, Moscow (2004).Google Scholar
  14. 14.
    S. Kikuchi, “On metrical Finsler connections of generalized Finsler spaces,” in: Proc. 5th Nat. Sem. Finsler and Lagrange Spaces in Honour 60th Birthday of Prof. Radu Miron, Brasov, February 10–15, 1988, Brasov (1989), pp. 197–206.Google Scholar
  15. 15.
    M. S. Knebelman, “Collineations and motions in generalized spaces,” Am. J. Math., 51, 527–564 (1929).CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    M. Matsumoto, “On Einstein’s gravitational field equation in a tangent Riemannian space of a Finsler space,” Repts. Math. Phys., 8, No. 1, 103–108 (1975).CrossRefMATHGoogle Scholar
  17. 17.
    M. Matsumoto, Foundation of Finsler Geometry and Special Finsler Spaces, Kaiseisha Press (1986).Google Scholar
  18. 18.
    M. Matsumoto, “The Tavakol van den Bergh conditions in the theories of gravity and projective changes of Finsler metrics,” Publ. Math. Debrecen, 42, Nos. 1–2, 155–168 (1993).MATHMathSciNetGoogle Scholar
  19. 19.
    R. Miron, “Metrical Finsler structures and metrical Finsler connections,” J. Math. Kyoto. Univ., 23, 219–224 (1983).MATHMathSciNetGoogle Scholar
  20. 20.
    R. Miron, “On the Finslerian theory of relativity,” Tensor, 44, No. 1, 63–81 (1987).MATHMathSciNetGoogle Scholar
  21. 21.
    R. Miron, R. K. Tavakol, V. Balan, and I. Roxburgh, “Geometry of space time and generalized Lagrange gauge theory,” Publ. Math. Debrecen, 42, Nos. 3–4, 215–224 (1993).MATHMathSciNetGoogle Scholar
  22. 22.
    A. Moor, “Entwicklung einer Geometrie der allgemeiner metrischen Linienelement raume,” Acta Sci. Math., 17, Nos. 1–2, 85–120 (1956).MATHMathSciNetGoogle Scholar
  23. 23.
    S. Sasaki, “On the differential geometry of tangent bundles of Riemannian manifolds, I,” Tohoku Math. J., 10, No. 3, 338–354 (1958).CrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    I. Tashiro, “A theory of transformation groups on generalized spaces and applications to Finsler and Cartan spaces,” J. Math. Soc. Jpn., 11, No. 11, 42–71 (1959).CrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    H. S.Wang, “On Finsler spaces with completely integrable equations of Killing,” J. London Math. Soc., 22, 5–9 (1947).CrossRefMATHMathSciNetGoogle Scholar
  26. 26.
    S. Watanabe, “Generalized Finsler spaces conformal to a Riemannian space and the Cartan like connections,” An. Sti. Univ. Iasi. Sec. 1a, 30, No. 4, 95–98 (1984).MATHGoogle Scholar
  27. 27.
    K. Yano and E. T. Davies, “On the tangent bundles of Finsler and Riemannian manifolds,” Rend. Circ. Math., 12, No. 2, 211–228 (1963).CrossRefMATHMathSciNetGoogle Scholar

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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.M. V. Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Institute of Mechanics of the M. V. Lomonosov Moscow State UniversityMoscowRussia

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