Locally Symmetric Homogeneous Finsler Spaces

Let (M, F) be a connected Finsler space and d the distance function of (M, F). A Clifford translation is an isometry rho of (M, F) of constant displacement, in other words such that d(x, rho(x)) is a constant function on M. In this paper, we consider a connected simply connected symmetric Finsler space and a discrete subgroup Gamma of the full group of isometries. We prove that the quotient manifold (M, F)/Gamma is a homogeneous Finsler space if and only if Gamma consists of Clifford translations of (M, F). In the process of the proof of the main theorem, we classify all the Clifford translations of symmetric Finsler spaces.