ON THE GEODESICS AND S-CURVATURE OF A HOMOGENEOUS FINSLER SPACE WITH SQUARE-ROOT (α, β)-METRIC

In this paper, we consider the square-root (α; β)-metric F which satisfies F (α; β) = √α(α + β). We prove the existence of invariant vector fields on a homogeneous Finsler space with square-root metric. Then we obtain the explicit formula for the S-curvature and mean Berwald curvature of homogeneous Finsler space with square-root metric. We study geodesics and geodesic vectors for homogeneous squareroot (α; β)-metric.