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

2011/03/10 by Zhiqi Chen, Ke Liang, Chen, Zhiqi +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1103.1924

The previous version is included as a part of this version

openalex publication_date 2011/03/10 · arxiv created 2012/03/15 · arxiv updated 2012/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Naturally reductive metrics and Einstein metrics on compact Lie groups
• Curvatures of left invariant metrics on lie groups

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