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Pré-Publication, Document De Travail Année : 2004

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 and B.-L. Chen and X.-P. Zhu.
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Dates et versions

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

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Gilles Carron, Marc Herzlich. Conformally flat manifolds with nonnegative Ricci curvature. 2004. ⟨hal-00003011v1⟩
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