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

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

2009-10-16

arxiv.org/abs/0910.3176v2

J. Phys. A: Math. Theor. 43 (2010) 135207 (15pp)

Mathematics

Differential Geometry

16 pages, AMSLaTex. v2 is a minor revision: title changed, references updated, typos fixed; it matches the published version.

Scientific paper

10.1088/1751-8113/43/13/135207

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.

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