On the flag curvature of homogeneous Finsler space with some special $(\alpha, \beta)$-metrics

TL;DR

This paper derives explicit formulas for the flag curvature of homogeneous Finsler spaces equipped with specific $(eta)$-metrics, including infinite series and exponential types, and applies these to naturally reductive spaces.

Contribution

It provides new explicit formulas for flag curvature in homogeneous Finsler spaces with special $(eta)$-metrics, extending understanding of their geometric properties.

Findings

Explicit formula for flag curvature with infinite series $(eta)$-metric.

Explicit formula for flag curvature with exponential $(eta)$-metric.

Application of formulas to naturally reductive homogeneous Finsler spaces.

Abstract

In this paper, first we derive an explicit formula for the flag curvature of a homogeneous Finsler space with infinite series $(\alpha, \beta)$-metric and exponential metric. Next, we deduce it for naturally reductive homogeneous Finsler space with the above mentioned metrics.