Canad. Math. Bull. 55(2012), 870-881
Printed: Dec 2012
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.
Einstein-Randers metric, compact Lie groups, geodesic, flag curvature
17B20 - Simple, semisimple, reductive (super)algebras
22E46 - Semisimple Lie groups and their representations
53C12 - Foliations (differential geometric aspects) [See also 57R30, 57R32]