| S~n中具Moebius平坦法丛的子流形 |
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| 引用本文： | 舒世昌,刘三阳.S~n中具Moebius平坦法丛的子流形[J].数学学报,2005,48(6):1221-1232. |
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| 作者姓名： | 舒世昌 刘三阳 |
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| 作者单位： | 咸阳师范学院数学系，西安电子科技大学应用数学系 咸阳 712000，西安 710071 |
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| 基金项目： | 国家自然科学基金资助项目（69972036）;陕西省自然科学基金资助项目（2003A02）;陕西省教育厅自然科学基金资助项目（2003JK215） |
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| 摘 要： | 本文研究S~n中不含脐点、Moebius形式为零且具Moebius平坦法丛的子流形的Moebius特性。分别利用子流形的Moebius Ricci曲率与Blaschke张量、Moebius标准数量曲率以及Blaschke张量与Moebius标准数量曲率之间所满足的某种内蕴关系刻画了S~n中子流形的Moebius特性,得到了S~n中法丛平坦子流形的两个分类定理。
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| 关 键 词： | Moebius度量 Moebius平坦法丛 Blaschke张量 |
| 文章编号： | 0583-1431（2005）06-1221-12 |
| 收稿时间： | 2004-10-26 |
| 修稿时间： | 2004-10-262005-05-31 |
Submanifolds with Moebius Flat Normal Bundle in S~n |
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| Shi Chang SHU.Submanifolds with Moebius Flat Normal Bundle in S~n[J].Acta Mathematica Sinica,2005,48(6):1221-1232. |
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| Authors: | Shi Chang SHU |
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| Institution: | Shi Chang SHU Department of Mathematics, Xianyang Teacher's College, Xianyang 712000, P. R. China San Yang LIU Department of Applied Mathematics, Xidian University, Xi'an 710071, P. R. China |
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| Abstract: | In this paper, we study the Moebius characterization of submanifolds in S~n without umbilic points and with vanishing Moebius form and fiat normal bundle. We give some Moebius characterizations of submanifolds by making use of the rigidity relations among Moebius Ricci curvature, Blaschke tensor and Moebius normalized scalar curvature as well as the rigidity relations between Blaschke tensor and Moebius normalized scalar curvature. We obtain two classification theorems of submanifolds with flat normal bundle in S~n. |
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| Keywords: | Moebius metric Moebius flat normal bundle Blaschke tensor |
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