Necessary and sufficient conditions for two dimensional $(\alpha,\beta)$-metrics with reversible geodesics

TL;DR

This paper investigates the specific conditions under which two-dimensional Finsler surfaces with $(eta,eta)$-metrics have reversible geodesics, providing a complete characterization of such metrics.

Contribution

It establishes necessary and sufficient conditions for $(eta,eta)$-metrics on Finsler surfaces to possess reversible geodesics, advancing the understanding of Finsler geometry.

Findings

Derived explicit conditions for reversibility of geodesics

Characterized $(eta,eta)$-metrics with reversible geodesics

Enhanced understanding of Finsler surface geometry

Abstract

We study the necessary and sufficient conditions for a Finsler surface with $(\alpha,\beta)$-metrics to be with reversible geodesics.