The characterization of Finsler spaces with Ricci curvature is an ancient and cumbersome one. In this paper, we have derived an expression of Ricci curvature for the homogeneous generalized Matsumoto change. Moreover, we have deduced the expression of Ricci curvature for the aforementioned space with vanishing the S-curvature. These findings contribute significantly to understanding the complex nature of Finsler spaces and their curvature properties.

The curvature characteristics of particular classes of Finsler spaces, such as homogeneous Finsler spaces, are one of the major issues in Finsler geometry. In this paper, we have obtained the expression for S-curvature in homogeneous Finsler space with a generalized Matsumoto metric and demonstrated that the homogeneous generalized Matsumoto space with isotropic S-curvature has to vanish the S-curvature. We have also derived the expression for the mean Berwald curvature by using the formula of S-curvature.