The decomposition of a Lie group with a left invariant pseudo-Riemannian metric and the uniqueness

Details The decomposition of a Lie group with a left invariant pseudo-Riemannian metric and the uniqueness The decomposition of a Lie group with a left invariant pseudo-Riemannian metric and the uniqueness

2011-03-10

arxiv.org/abs/1103.1924v2

Mathematics

Group Theory

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Scientific paper

In this paper, we discuss the decomposition of a Lie group with a left invariant pseudo-Riemannian metric and the uniqueness. In fact, it is a decomposition of a Lie group into totally geodesic sub-manifolds which is different from the De Rham decomposition on a Lie group. As an application, we give a decomposition of a Lie group with a left invariant pseudo-Riemannian Einstein metric, and prove that the decomposition is unique up to the order of the parts in the decomposition.

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