S^(n+1)上具有三个互异常仿Blaschke特征值的超曲面

The Hypersurfaces in S^(n+1)with Three Distinct Constant Para-Blaschke Eigenvalues

设x∶M→S^(n+1)是(n+1)-维单位球面上不含脐点的超曲面.在S^(n+1)的Mbius变换群下浸入x的四个基本不变量是:Mbius度量g;Mbius第二基本形式B;Mbius形式φ和Blaschke张量A.对称的(0,2)张量D=A+λB也是Mbius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→S^(n+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.

Let x：M^n→S^n＋1 be a hypersurface in the（n ＋ l）-dimensional unit sphere S^n＋1 without umbilics.Four basic invariants of x under the Mbius transformation group in S^n＋1 are Mbius metric g,Mbius second fundamental form B; Mbius formΦ;Blaschke tensor A.Let D = A ＋ AB,where A is a constant,then D is a symmetric（0,2） tensor and a Mbius invariant.D is called para-Blaschke tensor of x,the eingenvalues of D is called para-Blaschke eingenvalues of x.IfΦ= 0,and the para-Blaschke eingenvalues are constant.Then the hypersurface x：M^n→S^n＋1 is called para-Blaschke isoparametric hypersurface.In this paper,we classify the paraBlaschke isoparametric hypersurfaces with three distinct para-Blaschke eingenvalues such that one of them is simple.