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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 26, Issue 5


Clifford–Wolf translations of Finsler spaces

Shaoqiang Deng / Ming Xu
Published Online: 2012-04-26 | DOI: https://doi.org/10.1515/forum-2012-0032


In this paper, we study Clifford–Wolf translations of Finsler spaces. We give a characterization of those Clifford–Wolf translations generated by Killing vector fields. In particular, we show that there is a natural interrelation between the local one-parameter groups of Clifford–Wolf translations and the Killing vector fields of constant length. In the special case of homogeneous Randers spaces, we give some explicit sufficient and necessary conditions for a Killing vector field to have a constant length, in which case the local one-parameter group of isometries generated by the Killing field consist of Clifford–Wolf translations. Finally, we construct explicit examples to explain some of the results of this paper.

Keywords: Finsler spaces; Clifford–Wolf translations; Killing vector fields; homogeneous Randers manifolds

MSC: 22E46; 53C30

About the article

Received: 2012-03-18

Revised: 2012-04-04

Published Online: 2012-04-26

Published in Print: 2014-09-01

Funding Source: NSFC

Award identifier / Grant number: 10671096

Funding Source: NSFC

Award identifier / Grant number: 10971104

Funding Source: SRFDP of China

Citation Information: Forum Mathematicum, Volume 26, Issue 5, Pages 1413–1428, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0032.

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