| 非负Ricci曲率开流形的拓扑 |
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| 引用本文： | 杨芳云,徐森林,王作勤. 非负Ricci曲率开流形的拓扑[J]. 数学研究, 2003, 36(1): 1-7 |
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| 作者姓名： | 杨芳云 徐森林 王作勤 |
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| 作者单位： | 1. 中国科学技术大学数学系,安徽,合肥,230026
2. 华中师范大学数学系,湖北,武汉,430079 |
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| 基金项目： | National Natural Science Foundation of China (19971081) |
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| 摘 要： | 我们证明了对于具有非负Rieei曲率,大体积增长且内半径下有界的完备n维Riemann流形,只要存在常数C>0使得 则它微分同胚于欧式空间Rn.我们还证明了在某些pinching条件下具有非负射线曲率的完备n维Riemarm流形微分同胚与Rn,改进了已知的结果.
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| 关 键 词： | Excess函数 大体积增长 射线曲率 体积比较定理 Ricci曲率 开流形 拓扑 Riemann流形 欧式空间 |
The Topology of Open Manifolds with Nonnegative Ricci Curvature |
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| Yang Fangyun Xu Senlin Wang Zuoqin. The Topology of Open Manifolds with Nonnegative Ricci Curvature[J]. Journal of Mathematical Study, 2003, 36(1): 1-7 |
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| Authors: | Yang Fangyun Xu Senlin Wang Zuoqin |
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| Abstract: | In this paper > we prove that a complete n-dimensional Riemannian manifold with non-negative Ricci curvature, large volume growth and injectivity radius bounded from below is diffeomor-phic to R" provided that for some constant C>0. We alsoprove that a complete ?dimensional Riemannian manifold with nonnegative radial curvature Kmin, and under some pinched conditions is diffeomorphic to Rn. |
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| Keywords: | Excess function large volume growth radial curvature volume com- parison theorem |
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