Clifford-Wolf translations of Homogeneous Randers spheres

TL;DR

This paper provides a complete classification of Clifford-Wolf translations for homogeneous Randers metrics on spheres, revealing new phenomena where some CW-homogeneous Randers spaces are not symmetric, unlike in Riemannian geometry.

Contribution

It offers a comprehensive description of Clifford-Wolf translations on homogeneous Randers spheres and uncovers non-symmetric CW-homogeneous Randers spaces.

Findings

Complete classification of Clifford-Wolf translations on spheres

Discovery of non-symmetric CW-homogeneous Randers spaces

Contrast with Riemannian geometry where CW-homogeneity implies symmetry

Abstract

In this paper, we study Clifford-Wolf translations of homogeneous Randers metrics on spheres. It turns out that we can present a complete description of all the Clifford-Wolf translations of all the homogeneous Randers metrics on spheres. The most important point of this paper is that a new phenomena surfaces. Namely, we find that there are some CW-homogeneous Randers spaces which are essentially not symmetric. This is a great difference compared to Riemannian geometry, where any CW-homogeneous Riemannian manifold must be locally symmetric.