Geodesic Orbit Metrics on Compact Simple Lie Groups arising from Generalized Flag Manifolds

2018/05/04 by Huibin Chen, Chen, Huibin, Zhiqi Chen +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1805.01582

openalex publication_date 2018/05/04 · openalex created_date 2018/05/17 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate left-invariant geodesic orbit metrics on connected simple Lie groups, where the metrics are formed by the structures of generalized flag manifolds. We prove that all these left-invariant geodesic orbit metrics on simple Lie groups are naturally reductive.

Citations

• Naturally reductive metrics and Einstein metrics on compact Lie groups

Related

• Geodesic orbit metrics on the compact Lie group G₂
• Geodesic orbit spaces in real flag manifolds
• On a class of geodesic orbit spaces with abelian isotropy subgroup
• Geodesic orbit spaces of compact Lie groups of rank two
• Semi-Riemannian metrics on compact simple Lie Groups