Concavity and rigidity in non-negative curvature

Luigi Verdiani, Wolfgang Ziller

Published 2010-12-10, updated 2012-03-23Version 2

This is a significantly improved version with new applications. We show that there are many cohomogeneity one manifolds which do not admit an analytic invariant metric with non-negative sectional curvature, although they do have a smooth one. In particular, there are no invariant metric with positive curvature.