Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-13T07:27:10.537Z Has data issue: false hasContentIssue false

Conformally flat manifolds with nonnegative Ricci curvature

Published online by Cambridge University Press:  17 May 2006

Gilles Carron
Affiliation:
Laboratoire Jean Leray, UMR 6629 du CNRS, Université de Nantes, 44322 Nantes cedex 3, Francegilles.carron@math.sciences.univ-nantes.fr
Marc Herzlich
Affiliation:
Institut de Mathématiques et Modélisation de Montpellier, UMR 5149 du CNRS, Université Mont­pellier II, 34095 Montpellier cedex 5, Franceherzlich@math.univ-montp2.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that complete conformally flat manifolds of dimension $n\geq 3$ with nonnegative Ricci curvature enjoy nice rigidity properties: they are either flat, or locally isometric to a product of a sphere and a line; or are globally conformally equivalent to ${\mathbb R}^n$ or to a spherical spaceform ${\mathbb S}^n/\Gamma$. This extends previous results due to Cheng, Noronha, Chen, Zhu and Zhu.

Type
Research Article
Copyright
Foundation Compositio Mathematica 2006