Concavity and rigidity in non-negative curvature
Differential Geometry
2014-08-06 v2
Abstract
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.
Cite
@article{arxiv.1012.2265,
title = {Concavity and rigidity in non-negative curvature},
author = {Luigi Verdiani and Wolfgang Ziller},
journal= {arXiv preprint arXiv:1012.2265},
year = {2014}
}