Nonnegative Curvature, Symmetry and Fundamental Group

Abstract

We prove a result on equivariant deformations of flat bundles, and as a corollary, we obtain two ‘splitting in a finite cover’ theorems for isometric group actions on Riemannian manifolds with infinite fundamental groups, where the manifolds are either compact of Ric ≥ 0, or complete of sec ≥ 0. The result is used to construct Lie group actions that are isometric in some metric of scal > 0 and that are not isometric in any metric of Ric ≥ 0.