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

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.

29 pages