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Finsler spaces whose geodesics are orbits
Yan Zaili 1, Deng Shaoqiang 2 *
1. School of Mathematical Sciences, Nankai University, Tianjin 300071
2. School of Mathematical Sciences, Nankai University, Tianjin 300071
*Correspondence author
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Funding: none
Opened online:27 December 2013
Accepted by: none
Citation: Yan Zaili, Deng Shaoqiang.Finsler spaces whose geodesics are orbits[OL]. [27 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4577148
 
 
n this paper, we study Finsler spaces whose geodesics are the orbits of one-parameter subgroups of the group of isometries (abbreviated as Finsler g.o. spaces). We first generalize some geometric results on Riemannian g.o. spaces to the Finslerian setting. Then we show that a Finsler g.o. nilmanifold is at most two step nilpotent and construct some examples of g.o. spaces which are neither Berwaldian nor weakly symmetric. Further, we give a sufficient and necessary condition for a Randers space to be a g.o. space.
Keywords:Finsler g.o. spaces; nilmanifolds; Randers metrics.
 
 
 

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