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Conformally flat manifolds with nonnegative Ricci curvature

Gilles Carron·Marc Herzlich
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Abstract

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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Gilles Carron, Marc Herzlich. 2004-10-08. Conformally flat manifolds with nonnegative Ricci curvature. https://arxiv.org/abs/math/0410180

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