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arXiv:1401.8149 [math.DG]AbstractReferencesReviewsResources

Geodesics and Jacobi fields of pseudo-Finsler manifolds

Miguel Angel Javaloyes, Bruno Learth Soares

Published 2014-01-31, updated 2015-03-10Version 3

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.

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
Categories: math.DG
Subjects: 53C22, 53C50, 53C60, 58B20
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