English

Geodesics and Jacobi fields of pseudo-Finsler manifolds

Differential Geometry 2015-03-11 v3

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.

Keywords

Cite

@article{arxiv.1401.8149,
  title  = {Geodesics and Jacobi fields of pseudo-Finsler manifolds},
  author = {Miguel Angel Javaloyes and Bruno Learth Soares},
  journal= {arXiv preprint arXiv:1401.8149},
  year   = {2015}
}

Comments

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