Geodesics and Jacobi fields of pseudo-Finsler manifolds
  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. 
Miguel Angel Javaloyes and Bruno Learth Soares
math.DG