Pseudo-Conformal Actions of the Möbius Group

2023/05/30 by Mehdi Belraouti, Mohamed Deffaf, Belraouti, Mehdi +5 · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2305.18868

openalex publication_date 2023/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study compact connected pseudo-Riemannian manifolds (M,g) on which the conformal group Conf(M,g) acts essentially and transitively. We prove, in particular, that if the non-compact semi-simple part of Conf(M,g) is the Möbius group, then (M,g) is conformally flat.

Cited by

• Pseudo-Conformal actions of semisimple Lie groups
• Semi-Riemannian metrics on compact simple Lie Groups

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• Lorentzian manifolds with transitive conformal group