Pseudo-Conformal actions of semisimple Lie groups

2025/11/20 by Mehdi Belraouti, Belraouti, Mehdi, Mohamed Deffaf +3
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2511.16146

openalex publication_date 2025/11/20 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28

Abstract

We consider the pseudo-Riemannian Lichnerowicz conjecture in the homogeneous setting. In particular, we show that any compact connected pseudo-Riemannian manifold M on which a semisimple group G acts conformally, essentially and transitively, is conformally flat.

Citations

• Semi-Riemannian metrics on compact simple Lie Groups
• On homogeneous holomorphic conformal structures
• Pseudo-Conformal Actions of the Möbius Group
• The Lorentzian Lichnerowicz Conjecture for real-analytic, three-dimensional manifolds
• About pseudo-Riemannian Lichnerowicz conjecture

Related

• About pseudo-Riemannian Lichnerowicz conjecture
• Pseudo-Conformal Actions of the Möbius Group
• Conformal quotients of plane waves, and Lichnerowicz conjecture in a locally homogeneous setting
• On homogeneous holomorphic conformal structures
• The Lorentzian Lichnerowicz Conjecture for real-analytic, three-dimensional manifolds