Some Finsler spaces with homogeneous geodesics

Abstract

A geodesic in a homogeneous Finsler space is called a homogeneous geodesic if it is an orbit of a one‐parameter subgroup of G. A homogeneous Finsler space is called Finsler g.o. space if its all geodesics are homogeneous. Recently, the author studied Finsler g.o. spaces and generalized some geometric results on Riemannian g.o. spaces to the Finslerian setting. In the present paper, we investigate homogeneous geodesics in homogeneous spaces, and obtain the sufficient and necessary condition for an space to be a g.o. space. As an application, we get a series of new examples of Finsler g.o. spaces.