Naturally reductive pseudo Riemannian 2-step nilpotent Lie groups

2009/11/20 by Gabriela P. Ovando, Ovando, Gabriela P. · 2 citations
Mathematics · Physics and Astronomy · #22E25 #53B30 #53C30 #53C50 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0911.4067

openalex publication_date 2009/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with naturally reductive pseudo-Riemannian 2-step nilpotent Lie groups (N, \la , \ra_N), such that \la , \ra_N is invariant under a left action. The case of nondegenerate center is completely characterized. In fact, whenever \la , \ra_N restricts to a metric in the center it is proved here that the simply connected Lie group N can be constructed starting from a real representation (π,\vv) of a certain Lie algebra \ggo. We study the geometry of (N, \la , \ra_N) and we find the corresponding naturally reductive homogeneous structure. On the other hand, related to the case of degenerate center we provide another family of naturally reductive spaces, both non compact and also compact examples.

Citations

• Ricci flat left invariant Lorentzian metrics on 2-step nilpotent Lie\n groups
• Naturally reductive metrics and Einstein metrics on compact Lie groups

Cited by

• The distribution of symmetry of Lorentzian naturally reductive nilmanifolds
• Geodesic orbit pseudo-Riemannian H-type nilmanifolds: case of minimal admissible Clifford modules

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