设x:Mn→Sn 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=A+λB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:M→Sn+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 : Mn→Sn+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 : Mn→Sn+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
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Key words
Möbius metric /
Möbius form /
Blaschke tensor
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参考文献
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脚注
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基金
江西省自然科学基金资助项目(20122BAB201014)
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