| 徐森林,梅加强.Ricci曲率平行的一类Riemann流形的C∞紧性[J].数学研究及应用,2001,21(2):165~170 |
| Ricci曲率平行的一类Riemann流形的C∞紧性 |
| C∞ Compactness for a Class of Riemannian Manifolds with Parallel Ricci Curvature |
| 投稿时间：1998-05-29 |
| DOI：10.3770/j.issn:1000-341X.2001.02.002 |
| 中文关键词: |
| 英文关键词:sectional curvature Ricci curvature injectivity radius diameter volume Jacobi field. |
| 基金项目: |
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| 中文摘要: |
| 本文证明，在Gromov-Hausdorff拓扑下，Ricci曲率平行，截面曲率和单一半径有下界，体积有上界的Riemann流形的集合是c∞紧的.作为应用，我们证明一个pinching结果，即在某些条件下，Ricci平坦的流形必定平坦. |
| 英文摘要: |
| In this paper we prove that the set of Riemannian manifolds with parallel Ricci curvature, lower bounds for sectional curvature and injectivity radius and a upper bound for volume is c∞ compact in Gromov-Hausdroff topology. As an application we also prove a pinching result which states that a Ricci flat manifold is flat under certain conditions. |
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