| The Hypersurfaces in a Unit Sphere with Nonnegative Mobius Sectional Curvature |
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| 作者姓名： | 钟定兴 孙弘安 |
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| 作者单位： | Department of Mathematics, Gannan Teachers＇ College, Ganzhou, 341000 |
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| 基金项目： | Foundation item： The NNSF （10671087） of China and the NNSF （0511008） of Jiangxi Province, China. |
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| 摘 要： | Let x ： M→S^n＋1 be a hypersurface in the （n ＋ 1）-dimensional unit sphere S^n＋1 without umbilic point. The Mobius invariants of x under the Mobius transformation group of S^n＋1 are Mobius metric, Mobius form, Mobius second fundamental form and Blaschke tensor. In this paper, we prove the following theorem： Let x ： M→S^n＋1 （n≥2） be an umbilic free hypersurface in S^n＋1 with nonnegative Mobius sectional curvature and with vanishing Mobius form. Then x is locally Mobius equivalent to one of the following hypersurfaces： （i） the torus S^k（a） × S^n-k（√1- a^2） with 1 ≤ k ≤ n - 1; （ii） the pre-image of the stereographic projection of the standard cylinder S^k × R^n-k belong to R^n＋1 with 1 ≤ k ≤ n- 1; （iii） the pre-image of the stereographic projection of the Cone in R^n＋1 ： -↑x（u, v, t） = （tu, tv）, where （u,v, t）∈S^k（a） × S^n-k-1（ √1-a^2）× R^＋.
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| 关 键 词： | 单位球面 超曲面 麦比乌斯截面曲率 麦比乌斯型 非负形式 |
| 文章编号： | 1000-1778（2007）01-0015-09 |
| 收稿时间： | 2005-11-15 |
| 修稿时间： | 2005-11-15 |
The Hypersurfaces in a Unit Sphere with Nonnegative Mobius Sectional Curvature |
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| ZHONG Ding-xing,SUN Hong-an.The Hypersurfaces in a Unit Sphere with Nonnegative Mobius Sectional Curvature[J].Northeastern Mathematical Journal,2007,23(1):15-23. |
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| Authors: | ZHONG Ding-xing SUN Hong-an |
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| Abstract: | |
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| Keywords: | Mobius sectional curvature Mobius form Mobius second fundamental form Blaschke tensor |
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