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1 results

  • Conformally flat manifolds with nonnegative Ricci curvature

  • Gilles Carron, Marc Herzlich
  • Journal:
    Compositio Mathematica / Volume 142 / Issue 3 / May 2006
    Published online by Cambridge University Press:
    17 May 2006, pp. 798-810
    Print publication:
    May 2006
    • Article
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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.