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Left Invariant Einstein–Randers Metrics on Compact Lie Groups

Published online by Cambridge University Press:  20 November 2018

Hui Wang  and
Shaoqiang Deng
Hui Wang
Affiliation:
College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210003, P.R. Chinae-mail: wanghui0801@mail.nankai.edu.cn
Shaoqiang Deng
Affiliation:
College of Mathematics, Nankai University, Tianjin 300071, P.R. Chinae-mail: dengsq@nankai.edu.cn
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Abstract

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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.

Keywords

17B2022E4653C12Einstein–Randers metriccompact Lie groupsgeodesicflag curvature
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 4 , 01 December 2012 , pp. 870 - 881
Copyright
Copyright © Canadian Mathematical Society 2012

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