球面上具有四个不同主曲率的Moebius等参超曲面

The Moebius Isoparametric Hypersurfaces in S^(n+1) with Four Distinct Principal Curvatures

设x:M→S^(n+1)(n≥5)是(n+1)-维单位球面上不含脐点的超曲面,在S^(n+1)的Moebius变换群下浸入x的四个基本不变量是:Moebius度量g;Moebius第二基本形式B;Moebius形式Φ和Blaschke张量A.本文给出S^(n+1)上具有重数1,1,1,m(m≥2)的四个不同Moebius主曲率的Moebius等参超曲面的分类.

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 Moebius transformation group in S^n＋1 are Moebius metric g, Moebius second fundamental form 3; Moebius form Ф and Blaschke tensor A. We classify the Moebius isoparametric hypersurfaces in S^n＋1 with four distinct principal curvatures which multiplies are 1, 1, 1, m （m ≥ 2）.