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

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

2012-04-23

arxiv.org/abs/1204.5233v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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 $x_1, x_2\in M$ there is a Clifford-Wolf translation $\rho$ such that $\rho(x_1)=x_2$. 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.

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