Locally symmetric homogeneous Finsler spaces

Abstract

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.

Extends homogeneity criterion (known for Riemannian locally symmetric spaces) to Finsler locally symmetric spaces

Cited by in corpus (1)

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