Immersed Hypersurfaces in the Unit Sphere S^m+1 with Constant Blaschke Eigenvalues |
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作者姓名: | Xing Xiao LI Feng Yun ZHANG |
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作者单位: | Department of Mathematics, He'nan Normal University, Xinxiang 453007, He'nan, P. R. China |
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基金项目: | NSF of China (No. 10671181) |
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摘 要: | For an immersed submanifold x : M^m→ Sn in the unit sphere S^n without umbilics, an eigenvalue of the Blaschke tensor of x is called a Blaschke eigenvalue of x. It is interesting to determine all hypersurfaces in Sn with constant Blaschke eigenvalues. In this paper, we are able to classify all immersed hypersurfaces in S^m+1 with vanishing MSbius form and constant Blaschke eigenvalues, in case (1) x has exact two distinct Blaschke eigenvalues, or (2) m = 3. With these classifications, some interesting examples are also presented.
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关 键 词: | 单元球面 浸入超曲面 Blaschke本征值 Blaschke张量 |
修稿时间: | 2005-04-272005-09-14 |
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