# The Study of S - Curvature on a Homogeneous Finsler Space with Randers-Matsumoto Metric

## Keywords:

Randers-Matsumoto metric, Homogeneous Finsler space, invariant vector field, S-curvature, E-curvature## Abstract

In this article, we have focused on the study of S-curvature of Randers-Matsumoto metric on a homogeneous Finsler space. We have deduced the condition for an isometry of Finsler homogeneous space with Randers-Matsumoto metric to be an isometry of Riemannian homogeneous space and proved that the group of isometries of Finsler space are closed subgroups of that of Riemannian space. We have examined the existence of invariant vector field. Further, we have derived the formula for S-curvature on the reductive homogeneous space, discussed the condition for isotropic S-curvature and derived the E-curvature of the Randers-Matsumoto metric for the homogenous space by using S-curvature formula.

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