Abstract
In this paper, we obtain the first and the second variation of the energy functional of a pseudo-Finsler metric using the family of affine connec- tions associated to the Chern connection. This allows us to accomplish the computations with the free-coordinate methods of Modern Differential Ge- ometry. We also introduce the index form using the formula for the second variation and give some properties of Jacobi fields. Finally we prove that lightlike geodesics and its focal points are preserved up to reparametrization by conformal changes.
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