论文标题
具有非负N-Bakryémeryricci曲率的非划分空间的分裂定理和拓扑结构
The Splitting Theorem and Topology of Noncompact Spaces with Nonnegative N-Bakry Émery Ricci Curvature
论文作者
论文摘要
在本文中，我们将非负RICCI曲率的非绘制歧管闻名的拓扑结果概括为具有非负$ n $ bakryémeryémeryricci曲率的空间。我们研究了与非负$ n $ bakryémeryricci曲率的空间有关的分裂定理和称为无穷大属性的属性。此外，我们表明，如果$ m^n $是一个完整的，非算力的riemannian歧管，则具有非负$ n $ bakryémeryricci curvature，其中$ n> n $，则$ h_ {n-1}（m，mathbb {z}}）$是$ 0 $ $ 0 $。
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 $0$.
