Left Invariant Einstein-Randers Metrics on Compact Lie Groups

被引：9
|
作者：
Wang, Hui [1 ]
Deng, Shaoqiang [2 ]
机构：
[1] Nanjing Univ Posts & Telecommun, Coll Sci, Nanjing 210003, Jiangsu, Peoples R China
[2] Nankai Univ, Coll Math, Tianjin 300071, Peoples R China
来源：
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2012年 / 55卷 / 04期
关键词：
Einstein-Randers metric; compact Lie groups; geodesic; flag curvature; ISOMETRIES; GEODESICS;
D O I：
10.4153/CMB-2011-145-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study left invariant Einstein-Randers metrics on compact Lie groups. 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 simple Lie groups with the underlying Riemannian metric naturally reductive. Further, we completely determine the identity component of the group of isometries for this type of metrics on simple groups. Finally, we study some geometric properties of such metrics. In particular, we give the formulae of geodesics and flag curvature of such metrics.
引用
收藏
页码：870 / 881
页数：12
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