Hypersurfaces with isotropic Blaschke tensor

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概要

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• Let Mm be an m-dimensional submanifold without umbilical points in the m+1-dimensional unit sphere Sm+1. Three basic invariants of Mm under the Möbius transformation group of Sm+1 are a 1-form Φ called Möbius form, a symmetric (0,2) tensor A called Blaschke tensor and a positive definite (0,2) tensor g called Möbius metric. We call the Blaschke tensor is isotropic if there exists a function λ such that A = λg. One of the basic questions in Möbius geometry is to classify the hypersurfaces with isotropic Blaschke tensor. When λ is constant, the classification was given by Changping Wang and others. When λ is not constant, all hypersurfaces with dimensional m ≥ 3 and isotropic Blaschke tensor are explicitly expressed in this paper. Therefore, for the dimensional m ≥ 3, the above basic question is completely answered.

• 2011-10-01

著者

• Guo Zhen

  Department Of Electrical And Computer Engineering New Jersey Institute Of Technology

• Lin Limiao

  Department of Mathematics, Yunnan Normal University

• Guo Zhen

  Department Of Mathematics Yunnan Normal University

• Fang Jianbo

  Department Of Mathematics Yunnan Normal University

• Lin Limiao

  Department Of Mathematics Yunnan Normal University

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