Sn+1上具有三个互异常仿Blaschke特征值的超曲面

钟定兴, 孙弘安, 张祖锦

数学学报 ›› 2013, Vol. 56 ›› Issue (5) : 751-766.

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PDF(339 KB)
数学学报 ›› 2013, Vol. 56 ›› Issue (5) : 751-766. DOI: 10.12386/A2013sxxb0074
论文

Sn+1上具有三个互异常仿Blaschke特征值的超曲面

    钟定兴, 孙弘安, 张祖锦
作者信息 +

The Hypersurfaces in Sn+1 with Three Distinct Constant Para-Blaschke Eigenvalues

    Ding Xing ZHONG, Hong An SUN, Zu Jin ZHANG
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文章历史 +

摘要

x:MnSn 是(n+1)-维单位球面上不含脐点的超曲面. 在Sn+1的Möbius变换群下浸入x 的四个基本不变量是: Möbius 度量g;Möbius 第二基本形式B; Möbius形式Φ和Blaschke 张量A. 对称的(0,2)张量D=AB也是Möbius不变量, 其中λ是常数. D 称为浸入x的仿Blaschke 张量, 仿Blaschke 张量的特征值称为浸入x的仿Blaschke特征值. 如果Φ=0,对某常数λ, 仿Blaschke特征值为常数, 那么超曲面x:MSn+1称为仿 Blaschke等参超曲面. 本文对具有三个互异仿Blaschke 特征值(其中有一个重数为1)的仿Blaschke等参超曲面进行了分类.

Abstract

Let x : MnSn+1 be a hypersurface in the (n + 1)-dimensional unit sphere Sn+1 without umbilics. Four basic invariants of x under the Möbius transformation group in Sn+1 are Möbius metric g, Möbius second fundamental form B; Möbius form Φ; Blaschke tensor A. Let D = A + λB, where λ is a constant, then D is a symmetric (0; 2) tensor and a Möbius invariant. D is called para-Blaschke tensor of x, the eingenvalues of D is called para-Blaschke eingenvalues of x. If Φ= 0; and the para-Blaschke eingenvalues are constant. Then the hypersurface x : MnSn+1 is called para-Blaschke isoparametric hypersurface. In this paper, we classify the para-Blaschke isoparametric hypersurfaces with three distinct para-Blaschke eingenvalues such that one of them is simple.

关键词

Möbius 度量 / Möbius 形式 / Blaschke 张量

Key words

Möbius metric / Möbius form / Blaschke tensor

引用本文

导出引用
钟定兴, 孙弘安, 张祖锦. Sn+1上具有三个互异常仿Blaschke特征值的超曲面. 数学学报, 2013, 56(5): 751-766 https://doi.org/10.12386/A2013sxxb0074
Ding Xing ZHONG, Hong An SUN, Zu Jin ZHANG. The Hypersurfaces in Sn+1 with Three Distinct Constant Para-Blaschke Eigenvalues. Acta Mathematica Sinica, Chinese Series, 2013, 56(5): 751-766 https://doi.org/10.12386/A2013sxxb0074

参考文献

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基金

江西省自然科学基金资助项目(20122BAB201014)

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