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
收藏
页码：278 / 305
页数：28
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