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

共 50 条

[1] A pinching theorem for minimal hypersurfaces in a sphere
T. Hasanis
T. Vlachos
[J]. Archiv der Mathematik, 2000, 75 : 469 - 471
[2] A GLOBAL PINCHING THEOREM OF MINIMAL HYPERSURFACES IN THE SPHERE
SHEN, CL
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 105 (01) : 192 - 198
[3] An Eigenvalue Pinching Theorem for Compact Hypersurfaces in a Sphere
Hu, Yingxiang
Xu, Hongwei
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2017, 27 (03) : 2472 - 2489
[4] On the Second Pinching Theorem for Willmore Hypersurfaces in a Sphere
Haizhong Li
Meng Zhang
[J]. Results in Mathematics, 2024, 79
[5] On the Second Pinching Theorem for Willmore Hypersurfaces in a Sphere
Li, Haizhong
Zhang, Meng
[J]. RESULTS IN MATHEMATICS, 2024, 79 (03)
[6] An Eigenvalue Pinching Theorem for Compact Hypersurfaces in a Sphere
Yingxiang Hu
Hongwei Xu
[J]. The Journal of Geometric Analysis, 2017, 27 : 2472 - 2489
[7] A Pinching Theorem for Minimal Submanifolds in Sphere
许志才
[J]. Communications in Mathematical Research, 1998, (04) : 112 - 117
[8] A PINCHING THEOREM FOR MINIMAL SUBMANIFOLDS IN A SPHERE
XIA, CY
[J]. ARCHIV DER MATHEMATIK, 1991, 57 (03) : 307 - 312
[9] The second pinching theorem for hypersurfaces with constant mean curvature in a sphere
Hong-wei Xu
Zhi-yuan Xu
[J]. Mathematische Annalen, 2013, 356 : 869 - 883
[10] The second pinching theorem for hypersurfaces with constant mean curvature in a sphere
Xu, Hong-wei
Xu, Zhi-yuan
[J]. MATHEMATISCHE ANNALEN, 2013, 356 (03) : 869 - 883

← 1 2 3 4 5 →