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October, 2011 Hypersurfaces with isotropic Blaschke tensor
Zhen GUO, Jianbo FANG, Limiao LIN
J. Math. Soc. Japan 63(4): 1155-1186 (October, 2011). DOI: 10.2969/jmsj/06341155


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.


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Zhen GUO. Jianbo FANG. Limiao LIN. "Hypersurfaces with isotropic Blaschke tensor." J. Math. Soc. Japan 63 (4) 1155 - 1186, October, 2011.


Published: October, 2011
First available in Project Euclid: 27 October 2011

zbMATH: 1242.53010
MathSciNet: MR2855810
Digital Object Identifier: 10.2969/jmsj/06341155

Primary: 53A30
Secondary: 53B25

Keywords: Blaschke tensor , Möbius geometry

Rights: Copyright © 2011 Mathematical Society of Japan


Vol.63 • No. 4 • October, 2011
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