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

Mehdi Belraouti; Mohamed Deffaf; Yazid Raffed; Abdelghani Zeghib

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

Differential Geometry 2023-05-31 v1

Authors: Mehdi Belraouti , Mohamed Deffaf , Yazid Raffed , Abdelghani Zeghib

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.

Keywords

pseudo-riemannian manifolds conformal group mobius group conformally flat transitive action

Cite

@article{arxiv.2305.18868,
  title  = {Pseudo-Conformal Actions of the M{\"o}bius Group},
  author = {Mehdi Belraouti and Mohamed Deffaf and Yazid Raffed and Abdelghani Zeghib},
  journal= {arXiv preprint arXiv:2305.18868},
  year   = {2023}
}

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