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Conformally flat manifolds with nonnegative Ricci curvature

Published online by Cambridge University Press:  17 May 2006

Gilles Carron  and
Marc Herzlich
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
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Abstract

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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.

Keywords

conformally flat manifoldnonnegative Ricci curvature53C21 (primary)53C2453C15 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 3 , May 2006 , pp. 798 - 810
Copyright
Foundation Compositio Mathematica 2006