Conformally related invariant $(\alpha,\beta)$-metrics on homogeneous spaces

TL;DR

This paper derives the flag curvature formula for a class of Finsler metrics, studies their conformal relations on homogeneous spaces, and provides conditions and examples for conformally related $(eta)$-metrics.

Contribution

It introduces a comprehensive analysis of conformally related $(eta)$-metrics on homogeneous spaces, including curvature formulas and conformal conditions.

Findings

Derived flag curvature formula for $(eta)$-metrics of Berwald type.

Established necessary and sufficient conditions for conformal relations.

Presented examples of conformally related $(eta)$-metrics.

Abstract

In this paper, we give the flag curvature formula of general $(\alpha,\beta)$-metrics of Berwald type. We study conformally related $(\alpha,\beta)$-metrics, especially general $(\alpha,\beta)$-metrics that are conformally related to invariant $(\alpha,\beta)$-metrics. Also, a necessary and sufficient condition for a Finsler metric conformally related to an $(\alpha,\beta)$-metric is given, and conformally related Douglas Randers metrics are studied. Finally, we present some examples of conformally related $(\alpha,\beta)$-metrics.