# On the Reversible Geodesics for a Finsler space with Randers change of Quartic metric

## TL;DR

This paper investigates conditions under which a specific Finsler space with a Randers change of a quartic metric has reversible geodesics, exploring its geometric properties and the induced generalized distance.

## Contribution

It provides new conditions for reversibility of geodesics in a Finsler space with a quartic Randers metric and studies related geometric properties.

## Key findings

- Conditions for reversible geodesics are derived.
- The Finsler metric induces a generalized weighted quasi-distance.
- Geometric properties of the space with reversible geodesics are analyzed.

## 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.