Geodesics and Jacobi fields of pseudo-Finsler manifolds

2014/01/31 by Javaloyes, Miguel Angel, Soares, Bruno Learth · 2 citations
#53C22 #53C50 #53C60 #58B20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1401.8149

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.

Cited by

• On the space of cone geodesics and positive paths of contactomorphisms
• Special anisotropic conformal changes of conic pseudo-Finsler surfaces

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