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Left Invariant Einstein-Randers Metrics on Compact Lie Groups

  Published:2011-07-08
 Printed: Dec 2012
  • Hui Wang,
    College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210003, P.R. China
  • Shaoqiang Deng,
    College of Mathematics, Nankai University, Tianjin 300071, P.R. China
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Abstract

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: Einstein-Randers metric, compact Lie groups, geodesic, flag curvature Einstein-Randers metric, compact Lie groups, geodesic, flag curvature
MSC Classifications: 17B20, 22E46, 53C12 show english descriptions Simple, semisimple, reductive (super)algebras
Semisimple Lie groups and their representations
Foliations (differential geometric aspects) [See also 57R30, 57R32]
17B20 - Simple, semisimple, reductive (super)algebras
22E46 - Semisimple Lie groups and their representations
53C12 - Foliations (differential geometric aspects) [See also 57R30, 57R32]
 

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