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arXiv · 1612.00829

Pseudo-Finsler spaces modeled on a pseudo-Minkowski space

A. García-Parrado Gómez-Lobo·E. Minguzzi
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Abstract

We adopt a vierbein formalism to study pseudo-Finsler spaces modeled on a pseudo-Minkowski space. We show that it is possible to obtain closed expressions for most of the geometric objects of the theory, including Berwald's curvature, Landsberg's tensor, Douglas' curvature, non-linear connection and Ricci scalar. These expressions are particularly convenient in computations since they factor the dependence on the base and the fiber. As an illustration, we study Lorentz-Finsler spaces modeled on the Bogoslovsky Lorentz-Minkowski space, and give sufficient conditions which guarantee the Berwald property. We then specialize to a recently proposed Finslerian pp-wave metric. Finally, the paper points out that non-trivial Berwald spaces have necessarily indicatrices which admit some non-trivial linear group of symmetries.

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A. García-Parrado Gómez-Lobo, E. Minguzzi. 2016-12-02. Pseudo-Finsler spaces modeled on a pseudo-Minkowski space. https://doi.org/10.1016/s0034-4877(18)30069-7

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