A pinching theorem for minimal hypersurfaces in a sphere

被引：21

作者：

Hasanis, T ^{[1
]}

Vlachos, T ^{[1
]}

机构：

[1] Univ Ioannina, Dept Math, GR-45110 Ioannina, Greece

来源：

ARCHIV DER MATHEMATIK | 2000年 / 75卷 / 06期

关键词：

Fundamental Form; Principal Curvature; Minimal Hypersurface; Distinct Principal Curvature; Clifford Torus;

D O I：

10.1007/s000130050531

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study compact minimal hypersurfaces M-n in Sn+1 with two distinct principal curvatures and prove that if the squared norm S of the second fundamental form of M-n satisfies S greater than or equal to n, then S = n and M-n is a minimal Clifford torus.

引用

页码：469 / 471

页数：3