On the Class of Homogeneous Cubic Finsler Metrics Admitting (alpha, beta)-Types

Abstract

In this paper, we study the class of cubic metrics which are used in the theory of space-time structure and general relativity. We consider the homogeneous geodesics in the homogeneous cubic space. Let be a homogeneous cubic space and F defined by the Riemannian metric and the vector field . First, we show that is a geodesic vector of if and only if it is a geodesic vector of Also, we find a condition under which an arbitrary vector is a geodesic vector of cubic metric if and only if it is a geodesic vector of Riemannian metric. Then we show that, for Berwald type cubic metric, if the underlying Riemannian metric is naturally reductive, then the cubic metric is naturally reductive. Finally, we find the formula of the flag curvature of the class of cubic metrics.