The Splitting Theorem and topology of noncompact spaces with nonnegative N-Bakry Émery Ricci curvature,Proceedings of the American Mathematical Society

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The Splitting Theorem and topology of noncompact spaces with nonnegative N-Bakry Émery Ricci curvature
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-05-12 , DOI: 10.1090/proc/15240
Alice Lim

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 $0$.

中文翻译：

具有非负 N-Bakry Émery Ricci 曲率的非紧空间的分裂定理和拓扑

摘要：在本文中，我们将具有非负 Ricci 曲率的非紧流形的拓扑结果推广到具有非负 $N$-Bakry Émery Ricci 曲率的空间。我们研究了分裂定理和一个称为无穷大测地线循环的性质，与具有非负 $N$-Bakry Émery Ricci 曲率的空间有关。此外，我们证明如果 $M^n$ 是一个具有非负 $N$-Bakry Émery Ricci 曲率的完全非紧黎曼流形，其中 $N>n$，则 $H_{n-1}(M,\mathbb { Z})$ 是 $0$。

更新日期：2021-06-04

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