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arXiv · 1204.5048

Clifford-Wolf translations of Finsler spaces of negative flag curvature

Shaoqiang Deng
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Abstract

This paper has been withdrawn by the author due to a crucial sign error in equation 1. An isometry $ρ$ of a connected Finsler space $(M, F)$ is called bounded if the function $d(x, ρ(x))$ is bounded on $M$. It is called a Clifford-Wolf translation if the function $d(x, ρ(x))$ is constant on $M$. In this paper, we prove that on a complete connected simply connected Finsler space of non-positive flag curvature, an isometry is bounded if and only if it is a Clifford-Wolf translation. As an application, we prove that a homogeneous Finsler space of negative flag curvature admits a transitive solvable Lie group of isometries.

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Shaoqiang Deng. 2013-01-09. Clifford-Wolf translations of Finsler spaces of negative flag curvature. https://arxiv.org/abs/1204.5048

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