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arXiv · 1602.07724

Three-Dimensional Alexandrov spaces with positive or nonnegative Ricci curvature

Qintao Deng·Fernando Galaz-Garcia·Luis Guijarro·Michael Munn
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Abstract

We study closed three-dimensional Alexandrov spaces with a lower Ricci curvature bound in the $\mathsf{CD}^*(K,N)$ sense, focusing our attention on those with positive or nonnegative Ricci curvature. First, we show that a closed three-dimensional $\mathsf{CD}^*(2,3)$-Alexandrov space must be homeomorphic to a spherical space form or to the suspension of $\mathbb{R}P^2$. We then classify closed three-dimensional $\mathsf{CD}^*(0,3)$-Alexandrov spaces.

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Qintao Deng, Fernando Galaz-Garcia, Luis Guijarro, Michael Munn. 2016-02-24. Three-Dimensional Alexandrov spaces with positive or nonnegative Ricci curvature. https://arxiv.org/abs/1602.07724

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