Closed Willmore minimal hypersurfaces with constant scalar curvature in S5(1) are isoparametric

被引：10

作者：

Deng, Qintao ^{[1
,2
]}

Gu, Huiling ^{[3
]}

Wei, Qiaoyu ^{[1
]}

机构：

[1] Cent China Normal Univ, Sch Math & Stat, 152 Luoyu Rd, Wuhan 430079, Peoples R China

[2] Cent China Normal Univ, Hubei Key Lab Math Sci, 152 Luoyu Rd, Wuhan 430079, Peoples R China

[3] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2017年 / 314卷

关键词：

Willmore minimal hypersurfaces; Constant scalar curvature; Chern's conjecture; PINCHING CONSTANT;

D O I：

10.1016/j.aim.2017.05.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we will prove that any closed minimal Willmore hypersurface M-4 of S-5 with constant scalar curvature must be isoparametric. To be precise, M-4 is either an equatorial 4 sphere, a product of sphere S-2(root 2/2) x S-2(root 2/2) or a Cartan's minimal hypersurface. In particular, the value of the second fundamental form S can only be 0, 4, 12. This result strongly supports Chern's Conjecture. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：278 / 305

页数：28

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