Hypersurfaces with isotropic para-Blaschke tensor |
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Authors: | Jian Bo Fang Kun Zhang |
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Institution: | 1. Department of Mathematics and Statistics, Chuxiong Normal University, Chuxiong, 675000, P. R. China
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Abstract: | Let M n be an n-dimensional submanifold without umbilical points in the (n + 1)-dimensional unit sphere S n+1. Four basic invariants of M n under the Moebius transformation group of S n+1 are a 1-form Φ called moebius form, a symmetric (0, 2) tensor A called Blaschke tensor, a symmetric (0, 2) tensor B called Moebius second fundamental form and a positive definite (0, 2) tensor g called Moebius metric. A symmetric (0, 2) tensor D = A + µB called para-Blaschke tensor, where µ is constant, is also an Moebius invariant. We call the para-Blaschke tensor is isotropic if there exists a function λ such that D = λg. One of the basic questions in Moebius geometry is to classify the hypersurfaces with isotropic para-Blaschke tensor. When λ is not constant, all hypersurfaces with isotropic para-Blaschke tensor are explicitly expressed in this paper. |
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Keywords: | Moebius geometry para-Blaschke tensor isotropic |
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