Geodesic
Left Invariant Einstein–Randers Metrics on Compact Lie Groups
Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 870-881

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DOI

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.
DOI : 10.4153/CMB-2011-145-6
Mots-clés : 17B20, 22E46, 53C12, Einstein–Randers metric, compact Lie groups, geodesic, flag curvature 
Wang, Hui; Deng, Shaoqiang. Left Invariant Einstein–Randers Metrics on Compact Lie Groups. Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 870-881. doi: 10.4153/CMB-2011-145-6
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     author = {Wang, Hui and Deng, Shaoqiang},
     title = {Left {Invariant} {Einstein{\textendash}Randers} {Metrics} on {Compact} {Lie} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {870--881},
     year = {2012},
     volume = {55},
     number = {4},
     doi = {10.4153/CMB-2011-145-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-145-6/}
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