Concavity and rigidity in non-negative curvature

Luigi Verdiani; Wolfgang Ziller

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arXiv · 1012.2265

Concavity and rigidity in non-negative curvature

Luigi Verdiani·Wolfgang Ziller

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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.

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Luigi Verdiani, Wolfgang Ziller. 2010-12-10. Concavity and rigidity in non-negative curvature. https://arxiv.org/abs/1012.2265

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