Conformally flat manifolds with nonnegative Ricci curvature
Abstract
Description
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.
revised version, added reference to previous paper by S. Zhu on the same subject
revised version, added reference to previous paper by S. Zhu on the same subject