Locally symmetric homogeneous Finsler spaces

2012/06/16 by Deng, Shaoqiang, Wolf, Joseph A. · 1 citation
#22E46 #53C30 #53C35 #53C60 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1206.3685

Abstract

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

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