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Journal of Mathematical Physics / Volume 22 / Issue 5

J. Math. Phys. 22, 995 (1981); http://dx.doi.org/10.1063/1.525021 (10 pages)

Note on Finslerian relativity

Hirohisa Ishikawa

Department of Physics, Nagoya University, Nagoya, Japan

Finslerian structure of spacetime is investigated. For a special type of generalized Finsler metric the explicit expression of Cartan‐like metrical connection is derived and it is shown that it resembles the usual one. Causal problems in Finsler‐type spacetime are discussed and, based on the arguments, the Einstein‐type equations for the Finslerian quantities are derived by using the lifting of a Finsler metric to a tangent bundle. It is shown that a solution of the proposed equations can also be obtained from the complex structure of the tangent bundle. One‐form type metrics are used to discuss the geometrical interpretation of isosymmetry. A simple way of obtaining a metrical connection for a general generalized Finsler metric is given.

KEYWORDS and PACS

Keywords

SPACE−TIME, FIELD EQUATIONS, METRICS, UNIVERSE, RIEMANN SPACE, REVIEWS, MATHEMATICAL MANIFOLDS

PACS

  • 02.40.Ky

    Riemannian geometries

  • 04.20.Cv

    Fundamental problems and general formalism

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.525021

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

For access to fully linked references, you need to log in.
    H. Yukawa, Phys. Rev. 76, 300, 1731 (1949).

    D. K. Senet al. , J. Math. Phys. 12, 578 (1971JMAPAQ000012000004000578000001).

    K. Hayashi and T. Shirafuji, Phys. Rev. D 19, 3524 (1979).



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