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arXiv · 2001.06028

The Splitting Theorem and Topology of Noncompact Spaces with Nonnegative N-Bakry \'Emery Ricci Curvature

Alice Lim
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Abstract

In this paper, we generalize topological results known for noncompact manifolds with nonnegative Ricci curvature to spaces with nonnegative $N$-Bakry \'Emery 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 \'Emery Ricci Curvature. In addition, we show that if $M^n$ is a complete, noncompact Riemannian manifold with nonnegative $N$-Bakry \'Emery Ricci curvature where $N>n$, then $H_{n-1}(M,\mathbb{Z})$ is $0$.

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Alice Lim. 2020-01-16. The Splitting Theorem and Topology of Noncompact Spaces with Nonnegative N-Bakry \'Emery Ricci Curvature. https://arxiv.org/abs/2001.06028

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