Geodesics and Jacobi fields of pseudo-Finsler manifolds

Abstract

In this paper, we derive the first and the second variation of the energy functional for a pseudo-Finsler metric using the family of affine connections associated to the Chern connection. This opens the possibility to accomplish computations with coordinate-free methods. Using the second variation formula, we introduce the index form and present some properties of Jacobi fields.

arXiv comment24 pages, v2: minor changes, introduced a new Lemma 3.3 and Remark 3.6. v3: some changes of notation; last section has been removed