Clifford-Wolf translations of Finsler spaces of negative flag curvature

Details Clifford-Wolf translations of Finsler spaces of negative flag curvature Clifford-Wolf translations of Finsler spaces of negative flag curvature

2012-04-23

arxiv.org/abs/1204.5048v1

Mathematics

Differential Geometry

5 pages

Scientific paper

An isometry $\rho$ of a connected Finsler space $(M, F)$ is called bounded if the function $d(x, \rho(x))$ is bounded on $M$. It is called a Clifford-Wolf translation if the function $d(x, \rho(x))$ 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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