| 标量曲率衰竭的黎曼流形上的空隙定理 |
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| 引用本文： | 阮其华,陈志华. 标量曲率衰竭的黎曼流形上的空隙定理[J]. 同济大学学报(自然科学版), 2005, 33(10): 1401-1406 |
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| 作者姓名： | 阮其华 陈志华 |
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| 作者单位： | 1. 同济大学,应用数学系,上海,200092;莆田学院,数学系,福建,莆田,351100
2. 同济大学,应用数学系,上海,200092 |
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| 基金项目： | 国家自然科学基金资助项目(10271089)，福建省教育厅资助项目(JA04266) |
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| 摘 要： | 通过Yamabe流的研究,证明了对任一完备非紧局部共形平埋的黎曼流形,若Ricci曲率非负,标量曲率有界且它的平均值满足一定衰竭条件,则此流形是平坦的.
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| 关 键 词： | 空隙定理 标量曲率 Yamabe流 |
| 文章编号： | 0253-374X（2005）10-1401-06 |
| 收稿时间： | 2004-05-17 |
| 修稿时间： | 2004-05-17 |
Gap Theorem on Riemannian Manifold with Decaying Scalar Curvature |
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| RUAN Qi-hua,CHEN Zhi-hua. Gap Theorem on Riemannian Manifold with Decaying Scalar Curvature[J]. Journal of Tongji University(Natural Science), 2005, 33(10): 1401-1406 |
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| Authors: | RUAN Qi-hua CHEN Zhi-hua |
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| Affiliation: | 1. Department of Applied Mathematics,Tongji University,Shanghai 200092 ,China; 2. Department of Mathematics, Putian College, Putian 351100, China |
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| Abstract: | In this paper,through studying Yamabe flow,we prove that for any complete noncompact locally conformally flat manifolds,if the Ricci curvature is nonnegative,the scalar curvature is bounded and the mean value of the scalar curvature satisfies some decaying condition,then the manifold is flat. |
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| Keywords: | gap theorem scalar curvature Yamabe flow |
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