Curvature of submanifolds in point Finsler spaces

  • L. Tamássy
Part of the Mathematics and Its Applications book series (MAIA, volume 350)

Abstract

A point Finsler space is one in which vectors are defined at points and not at line-elements. We construct a curvature for submanifolds in these spaces endowed with a connection, and we show that this is a generalization of the Gauss curvature from Riemannian geometry.

Keywords

Gauss Curvature Fundamental Function Finsler Space Affine Connection Cartan Connection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    W. Barthel: Über die Parallelverschiebung mit Längeninvarianz in lokal-Minkowskischen Räumen I, II, Arch. Math. 4, (1953), 346–365.MathSciNetCrossRefGoogle Scholar
  2. 2.
    H. Gama: Theory of subspaces in areal spaces of the submetric class, Tensor 18, (1962), 168–180.MathSciNetGoogle Scholar
  3. 3.
    T. Igarashi: On Lie derivatives in areal spaces, Tensor 18, (1967), 205–211.MathSciNetMATHGoogle Scholar
  4. 4.
    R. S. Ingarden: Über die Einbettung eines Finslerschen Raumes in einem Minkowskischen, Raum. Bull. Acad. Polonaise CI. Ill 2, (1954), 305–308.MathSciNetMATHGoogle Scholar
  5. 5.
    R. S. Ingarden: On physical interpretation of Finsler and Kawaguchi geometries and the Barthel nonlinear connection, Tensor 46, (1987), 354–360.MathSciNetMATHGoogle Scholar
  6. 6.
    H. Iwamoto: On geometries associated with multiple integrals, Math. Japonica 1, (1948), 74–91.MathSciNetMATHGoogle Scholar
  7. 7.
    D. Laugwitz: Geometrical methods in the differential geometry of Finsler spaces, Geom. Calc. 1. 10 ciclo CIMEA, Ed. Cremonese, 1961Google Scholar
  8. 8.
    A. Kawaguchi: On areal spaces I. Metric tensors in n-dimensional spaces based on the notion of two-dimensional area, Tensor 1, (1950) 14–45.MathSciNetGoogle Scholar
  9. 9.
    A. Kawaguchi: On the theory of areal spaces, Bull Calcutta Math. Soc. 56 (1964), 91–107.MathSciNetMATHGoogle Scholar
  10. 10.
    M. Matsumoto: Theory of Y-extremal and minimal hypersurfaces in a Finler space, J. Math. Kyoto Univ. 26 (1986) 647–665.MathSciNetMATHGoogle Scholar
  11. 11.
    M. Matsumoto: Contributions of prescribed supporting element and the Cartan Yconnection, Tensor 49 (1990) 9–17.MathSciNetMATHGoogle Scholar
  12. 12.
    H. Rund: The differential geometry of Finsler spaces, Springer, Berlin, 1959.MATHGoogle Scholar
  13. 13.
    L. Tamássy: A characteristic property of the sphere, Pacific J. Math. 29 (1969), 439–446.MathSciNetMATHGoogle Scholar
  14. 14.
    L. Tamássy: Metric tensors of areal spaces, Tensor 31 (1978) 71–78.Google Scholar
  15. 15.
    L. Tamássy: Area and curvature in Finsler spaces, ROMP 33 (1993), 233–239.MATHGoogle Scholar
  16. 16.
    K. Tandai: On areal spaces VI, Tensor 3 (1954), 40–45.MathSciNetGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • L. Tamássy
    • 1
  1. 1.Institute of Mathematics and Informatics Lajos KossuthUniversity DebrecenDebrecen, Pf.12Hungary

Personalised recommendations