On the existence of homogeneous geodesic in homogeneous Finsler spaces

A connected Finsler space (M,F) is said to be homogeneous if it admits a transitive connected Lie group G of isometries. A geodesic in a homogeneous Finsler space is called homogeneous if it is an orbit of a one-parameter subgroup of G. In this paper, we prove that any homogeneous Finsler space admits at least one homogeneous geodesic through each point.