On $S$-Curvature of Homogeneous Finsler spaces with $(\alpha ,\beta )$-metrics

Abstract

The study of curvature properties of homogeneous Finsler spaces with $(\alpha ,\beta )$-metrics is one of the central problems in Riemann-Finsler geometry. In the present paper, the existence of invariant vector fields on homogeneous Finsler spaces with square $(\alpha ,\beta )$-metric and Randers changed square $(\alpha ,\beta )$-metric is proved. Further, an explicit formula for $S$-curvature of these $(\alpha ,\beta )$-metrics is established. Finally, using the formula of $S$-curvature, the mean Berwald curvature of afore said $(\alpha ,\beta )$-metrics is calculated.

21 pages