Anisotropic conformal invariance of lightlike geodesics in pseudo-Finsler manifolds

Abstract

In this paper, we prove that lightlike geodesics of a pseudo-Finsler manifold and its focal points are preserved up to reparametrization by anisotropic conformal changes, using the Chern connection and the anisotropic calculus and the fact that geodesics are critical points of the energy functional and Jacobi fields, the kernel of its index form. This result has applications to the study of Finsler spacetimes.

arXiv comment12 pages. arXiv admin note: text overlap with arXiv:1401.8149

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Cited by in corpus (6)

• On the definition and examples of cones and Finsler spacetimes
• Applications of cone structures to the anisotropic rheonomic Huygens' principle
• Anisotropic connections and parallel transport in Finsler spacetimes
• Anisotropic Conformal Dark Gravity on the Lorentz Tangent Bundle Spacetime
• On the Cut Locus of Submanifolds of a Finsler Manifold
• Lightlike hypersurfaces and time-minimizing geodesics in cone structures