On the Reversible Geodesics for a Finsler Space with Randers Change of Quartic metric

Gauree Shanker, Ruchi Kaushik Sharma

Abstract

In this paper, we consider a Finsler space with a Randers change of Quartic metric F = $\sqrt[4]{\alpha^4 + \beta^4} + \beta$. The conditions for this space to be with reversible geodesics are obtained. Further, we study some geometrical properties of F with reversible geodesics and prove that the Finsler metric F induces a generalized weighted quasi-distance $d_F$ on M.