Left Invariant Einstein-Randers Metrics on Compact Lie Groups

Canadian mathematical bulletin

Hui Wang¹  Shaoqiang Deng² 

[1] College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210003, P.R. China;College of Mathematics, Nankai University, Tianjin 300071, P.R. China

关键词: Einstein-Randers metric;    compact Lie groups;    geodesic;    flag curvature;   

DOI  :  10.4153/CMB-2011-145-6

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper we study left invariant Einstein-Randers metrics on compact Liegroups. First, we give a method to construct left invariant non-Riemannian Einstein-Randers metrics on a compact Lie group, using the Zermelo navigation data.Then we prove that this gives a complete classification of left invariant Einstein-Randers metrics on compact simpleLie groups with the underlying Riemannian metric naturally reductive. Further, we completely determine the identity component of the group ofisometries for this type of metrics on simple groups. Finally, we study somegeometric properties of such metrics. In particular, we give the formulae of geodesics and flag curvatureof such metrics.

【 授权许可】

Unknown