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arXiv 2001.060282020-01math.DG

The Splitting Theorem and Topology of Noncompact Spaces with Nonnegative N-Bakry Émery Ricci Curvature

Alice Lim

备注：: 17 pages, 4 figures, typos corrected, references added, sections rearranged. To appear in the Proceedings of the AMS

英文摘要：

In this paper, we generalize topological results known for noncompact manifolds with nonnegative Ricci curvature to spaces with nonnegative $N$-Bakry Émery Ricci curvature. We study the Splitting Theorem and a property called the geodesic loops to infinity property in relation to spaces with nonnegative $N$-Bakry Émery Ricci Curvature. In addition, we show that if $M^n$ is a complete, noncompact Riemannian manifold with nonnegative $N$-Bakry Émery Ricci curvature where $N>n$, then $H_{n-1}(M,\mathbb{Z})$ is $0$.

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