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Article Dans Une Revue Compositio Mathematica Année : 2006

Conformally flat manifolds with nonnegative Ricci curvature

Résumé

We show that complete conformally flat manifolds of dimension n>2 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 flat space or to a spherical spaceform. This extends previous works by Q.-M. Cheng, M.H. Noronha, B.-L. Chen and X.-P. Zhu, and S. Zhu.
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Dates et versions

hal-00003011 , version 1 (06-10-2004)
hal-00003011 , version 2 (08-10-2004)

Identifiants

Citer

Gilles Carron, Marc Herzlich. Conformally flat manifolds with nonnegative Ricci curvature. Compositio Mathematica, 2006, 142, pp.798-810. ⟨10.1112/S0010437X06002016⟩. ⟨hal-00003011v2⟩
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