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Clifford-Wolf translations of left invariant Randers metrics on compact Lie groups
| Content Provider | Semantic Scholar |
|---|---|
| Author | Deng, Shaoqiang Xu, Ming |
| Copyright Year | 2012 |
| 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 $x_1, x_2\in M$ 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. |
| Starting Page | 133 |
| Ending Page | 148 |
| Page Count | 16 |
| File Format | PDF HTM / HTML |
| DOI | 10.1093/qmath/hat003 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1204.5233v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1093/qmath%2Fhat003 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
