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, 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 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 nontrivial Berwald spaces have necessarily indicatrices which admit some nontrivial linear group of symmetries.
Reports on Mathematical Physics
- Pub Date:
- August 2018
- Finsler geometry;
- Minkowski space;
- Berwald space;
- Mathematics - Differential Geometry;
- General Relativity and Quantum Cosmology
- 15 pages, no figures. Accepted by "Reports on Mathematical Physics"