English

Ricci Bounds for Euclidean and Spherical Cones

Differential Geometry 2010-03-11 v1

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).

Keywords

Cite

@article{arxiv.1003.2114,
  title  = {Ricci Bounds for Euclidean and Spherical Cones},
  author = {Kathrin Bacher and Karl-Theodor Sturm},
  journal= {arXiv preprint arXiv:1003.2114},
  year   = {2010}
}

Comments

12 pages, 3 figures

R2 v1 2026-06-21T14:56:08.083Z