Finsler Spaces of Riemann-Minkowski Type

  • L. Tamássy
Chapter

Abstract

Performing centroaffine transformations in the tangent spaces of a locally euclidean space there results a Riemannian space. Performing this “Riemannian process” in a locally Minkowski space we obtain a Finsler space called of Riemann-Minkowski type. We show that the admission of a metrical linear parallel displacement (connection) of the tangent vectors characterizes this class of the Finsler spaces. We also show that in the case of the existence of a sufficiently wide family of rotations every Finsler space of Riemann-Minkowski type becomes, partially or totally, a Riemann space.

Keywords

Minkowski Space Affine Transformation Riemannian Space Linear Connection Finsler Space 
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.
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References

  1. [1]
    Gruber, P.M., Minimal ellipsoid and their duals, Rend. Circ. Math. Palermo, 37, (1988), 35–64.CrossRefGoogle Scholar
  2. [2]
    Ingarden, R.S. and Tamássy, L., The point Finsler spaces and their physical applications in electron optics and thermodynamics, Mathl. Comput. Modelling, 20, (1994), 93–107.CrossRefGoogle Scholar
  3. [3]
    Ichijyo, Y., Finsler manifolds modelled on Minkowski spaces, J. Math. Kyoto Univ., 16, (1976), 639–652;.Google Scholar
  4. [4]
    Ichijyo, Y., Finsler manifolds with a linear connection, J. Math. Tokushima Univ., 10, (1976), 1–11.Google Scholar
  5. [5]
    Kozma, L. and Baran, S., On metrical homogeneous connections of a Finsler point space, Publ. Math. Debrecen, 49, (1996), 59–68.Google Scholar
  6. [6]
    Matsumoto, M. and Shimada, H., On Finsler spaces with 1-form metric, Tensor N. S., 32, (1978), 161–169.Google Scholar
  7. [7]
    Matsumoto, M. and Shimada, H., On Finsler spaces with 1-form metric II, Tensor N. S., 32, (1978), 275–278.Google Scholar
  8. [8]
    Miron, R. and Anastasiei, M., The Geometry of Lagrange Spaces, Kluwer Ac. Publ., Dodrecht, 1994.CrossRefGoogle Scholar
  9. [9]
    Szilasi, J., Notable Finsler connections on a Finsler manifold, Lecturas Matemáticas, 19, (1998), 7–34.Google Scholar
  10. [10]
    Tamássy, L., Curvature of submanifolds in point Finsler spacesv, New Developments in Diff. Geom., Proc. Coll. on Diff. Geom., Debrecen, July 1994, Kluwer Ac. Publ. 1996 391–397.Google Scholar
  11. [11]
    Tamássy, L., Area and metrical connections in Finsler spaces, Finslerian Geometries, Kluwer Ac. Publ., 109, Dodrecht, 2000, Proc. of Coll. on Finsler Spaces, Edmonton, 1998 July, pp. 263–280.Google Scholar
  12. [12]
    Tamássy, L., Point Finsler spaces with metrical linear connections, Publ. Math. Debrecen / 56, (2000), 643–655.Google Scholar
  13. [13]
    Thompson, A.C., Minkowski Geometry, Cambridge Univ. Press, Cambridge, 1996.CrossRefGoogle Scholar

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© Springer Science+Business Media New York 2003

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  • L. Tamássy

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