Conformally flat manifolds with nonnegative Ricci curvature
Differential Geometry
2007-05-23 v2
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.
Cite
@article{arxiv.math/0410180,
title = {Conformally flat manifolds with nonnegative Ricci curvature},
author = {Gilles Carron and Marc Herzlich},
journal= {arXiv preprint arXiv:math/0410180},
year = {2007}
}
Comments
revised version, added reference to previous paper by S. Zhu on the same subject