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Pseudo-Finsler Spaces Modeled on a Pseudo-Minkowski Space

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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… Click to show full 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.

Keywords: pseudo finsler; finsler spaces; minkowski space; spaces modeled

Journal Title: Reports on Mathematical Physics
Year Published: 2018

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