Finsler geodesics in the presence of a convex function and their applications

Abstract

We obtain a result about the existence of only a finite number of geodesics between two fixed non-conjugate points in a Finsler manifold endowed with a convex function. We apply it to Randers and Zermelo metrics. As a by-product, we also get a result about the finiteness of the number of lightlike and timelike geodesics connecting an event to a line in a standard stationary spacetime.

16 pages, AMSLaTex. v2 is a minor revision: title changed, references updated, typos fixed; it matches the published version. This preprint and arXiv:math/0702323v3 [math.DG] substitute arXiv:math/0702323v2 [math.DG]

References in corpus (3)

• On the energy functional on Finsler manifolds and applications to stationary spacetimes
• A note on the existence of standard splittings for conformally stationary spacetimes
• Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric

Cited by in corpus (6)

• On Finsler spacetimes with a timelike Killing vector field
• Convex regions of stationary spacetimes and Randers spaces. Applications to lensing and asymptotic flatness
• Noncommutative black hole in the Finslerian spacetime
• A note on the Sagnac effect in general relativity as a Finslerian effect
• Harmonic Coordinates for the Nonlinear Finsler Laplacian and Some Regularity Results for Berwald Metrics
• Riemannian manifolds dual to static spacetimes