PseudoFinsler Spaces Modeled on a PseudoMinkowski Space
Abstract
We adopt a vierbein formalism to study pseudoFinsler spaces modeled on a pseudoMinkowski 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, nonlinear 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 LorentzFinsler spaces modeled on the Bogoslovsky LorentzMinkowski space, and give sufficient conditions which guarantee the Berwald property. We then specialize to a recently proposed Finslerian ppwave metric. Finally, the paper points out that nontrivial Berwald spaces have necessarily indicatrices which admit some nontrivial linear group of symmetries.
 Publication:

Reports on Mathematical Physics
 Pub Date:
 August 2018
 DOI:
 10.1016/S00344877(18)300697
 arXiv:
 arXiv:1612.00829
 Bibcode:
 2018RpMP...82...29G
 Keywords:

 Finsler geometry;
 Minkowski space;
 Berwald space;
 Mathematics  Differential Geometry;
 General Relativity and Quantum Cosmology
 EPrint:
 15 pages, no figures. Accepted by "Reports on Mathematical Physics"