Pseudo-Conformal Actions of the M{\"o}bius Group

Author:

Mehdi Belraouti, Mohamed Deffaf, Yazid Raffed, Abdelghani Zeghib

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG)

journal:

date:

2023-05-29 16:00:00

Abstract

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

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