The Splitting Theorem and topology of noncompact spaces with nonnegative N-Bakry Émery Ricci curvature

Lim, Alice

doi:10.1090/proc/15240

The Splitting Theorem and topology of noncompact spaces with nonnegative N-Bakry Émery Ricci curvature
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by Alice Lim

Proc. Amer. Math. Soc. 149 (2021), 3515-3529

DOI: https://doi.org/10.1090/proc/15240

Published electronically: May 12, 2021

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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 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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