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arXiv · 1003.2114

Ricci Bounds for Euclidean and Spherical Cones

Kathrin Bacher·Karl-Theodor Sturm
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Abstract

We prove generalized lower Ricci bounds for Euclidean and spherical cones over compact Riemannian manifolds. These cones are regarded as complete metric measure spaces. We show that the Euclidean cone over an n-dimensional Riemannian manifold whose Ricci curvature is bounded from below by n-1 satisfies the curvature-dimension condition CD(0,n+1) and that the spherical cone over the same manifold fulfills the curvature-dimension condition CD(n,n+1).

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Kathrin Bacher, Karl-Theodor Sturm. 2010-03-10. Ricci Bounds for Euclidean and Spherical Cones. https://arxiv.org/abs/1003.2114

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