Clifford-Wolf translations of left invariant Randers metrics on compact Lie groups

2012/04/23 by Deng, Shaoqiang, Xu, Ming
#22E46 #53C30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1204.5233

Abstract

A Clifford-Wolf translation of a connected Finsler space is an isometry which moves each point the sam distance. A Finsler space (M, F) is called Clifford-Wolf homogeneous if for any two point x₁, x₂∈ M there is a Clifford-Wolf translation ρ such that ρ(x₁)=x₂. In this paper, we study Clifford-Wolf translations of left invariant Randers metrics on compact Lie groups. The mian result is that a left invariant Randers metric on a connected compact simple Lie group is Clifford-Wolf homogeneous if and only if the indicatrix of the metric is a round sphere with respect to a bi-invariant Riemannian metric. This presents a large number of examples of non-reversible Finsler metrics which are Clifford-Wolf homogeneous.

Related

• Clifford-Wolf homogeneous left invariant (α,β)-metrics on compact semi-simple Lie groups
• Clifford-Wolf homogeneous Finsler metrics on spheres
• Clifford-Wolf homogeneous Randers spaces
• Clifford-Wolf translations of Homogeneous Randers spheres
• (α₁,α₂)-Spaces and Clifford-Wolf Homogeneity