Homogeneous Finsler spaces with some special $(\alpha, \beta)$-metrics

TL;DR

This paper investigates the geometric properties of homogeneous Finsler spaces equipped with specific $(eta)$-metrics, deriving formulas for $S$-curvature and mean Berwald curvature to deepen understanding of their structure.

Contribution

It establishes the existence of invariant vector fields and provides explicit formulas for $S$-curvature and mean Berwald curvature in these specialized Finsler spaces.

Findings

Existence of invariant vector fields on these spaces

Explicit formulas for $S$-curvature

Explicit formulas for mean Berwald curvature

Abstract

In this paper, first we prove the existence of invariant vector field on a homogeneous Finsler space with infinite series $(\alpha, \beta)$-metric and exponential metric. Next, we deduce an explicit formula for the the $S$-curvature of homogeneous Finsler space with these metrics. Using this formula, we further derive the formula for mean Berwald curvature of the homogeneous Finsler space with the above mentioned metrics.