Reversible Geodesics of a Finsler Space with (α,β)-Metric

Abstract

This paper deals with the existence of reversible geodesics over a Finsler space with some (α,β)-metrics. The conditions for a Finsler space (M,F) to be with reversible geodesics are obtained. We study some geometrical properties of F with reversible geodesics and prove that the Finsler metric F induces a weighted quasi-metric d_F on M.