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arXiv:math/0410180 [math.DG]AbstractReferencesReviewsResources

Conformally flat manifolds with nonnegative Ricci curvature

Gilles Carron, Marc Herzlich

Published 2004-10-06, updated 2004-10-08Version 2

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.

Comments: revised version, added reference to previous paper by S. Zhu on the same subject
Categories: math.DG
Subjects: 53C15, 53C24, 58J60
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