CURVATURE AND RIGIDITY THEOREMS OF SUBMANIFOLDS IN A UNIT SPHERE

被引：0
|
作者：
Shu, Shichang [1 ]
Li, Yanyan [1 ]
机构：
[1] Xianyang Normal Univ, Inst Math & Informat Sci, Xianyang 712000, Shaanxi, Peoples R China
来源：
BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 3卷 / 04期
关键词：
submanifolds; mean curvature; scalar curvature; rigidity theorems;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we investigate n-dimensional submanifolds with higher codimension in a unit sphere Sn+p (1). We obtain some rigidity results of submanifolds in Sn+p (1) with parallel mean curvature vector or with constant scalar curvature, which generalize some related rigidity results of hypersurfaces.
引用
收藏
页码：15 / 30
页数：16
相关论文
共 50 条
  • [1] Rigidity theorems for hypersurfaces with constant scalar curvature in a unit sphere
    Wei, Guoxin
    Suh, Young Jin
    [J]. GLASGOW MATHEMATICAL JOURNAL, 2007, 49 : 235 - 241
  • [2] Rigidity of Willmore submanifolds and extremal submanifolds in the unit sphere
    Deng-Yun Yang
    Hai-Ping Fu
    Jin-Guo Zhang
    [J]. Archiv der Mathematik, 2023, 121 : 329 - 342
  • [3] Rigidity of Willmore submanifolds and extremal submanifolds in the unit sphere
    Yang, Deng-Yun
    Fu, Hai-Ping
    Zhang, Jin-Guo
    [J]. ARCHIV DER MATHEMATIK, 2023, 121 (03) : 329 - 342
  • [4] GLOBAL RIGIDITY THEOREMS FOR SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE
    潘鹏飞
    许洪伟
    赵恩涛
    [J]. Acta Mathematica Scientia, 2023, 43 (01) : 169 - 183
  • [5] Global Rigidity Theorems for Submanifolds with Parallel Mean Curvature
    Pengfei Pan
    Hongwei Xu
    Entao Zhao
    [J]. Acta Mathematica Scientia, 2023, 43 : 169 - 183
  • [6] GLOBAL RIGIDITY THEOREMS FOR SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE
    Pan, Pengfei
    Xu, Hongwei
    Zhao, Entao
    [J]. ACTA MATHEMATICA SCIENTIA, 2023, 43 (01) : 169 - 183
  • [7] Rigidity of closed CSL submanifolds in the unit sphere
    Luo, Yong
    Sun, Linlin
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2023, 40 (03): : 531 - 555
  • [8] SOME SPHERE THEOREMS FOR SUBMANIFOLDS WITH POSITIVE BIORTHOGONAL CURVATURE
    Rufino, Elzimar
    [J]. GLASGOW MATHEMATICAL JOURNAL, 2017, 59 (03) : 717 - 728
  • [9] SUBMANIFOLDS WITH CONSTANT SCALAR CURVATURE IN A UNIT SPHERE
    Guo, Xi
    Li, Haizhong
    [J]. TOHOKU MATHEMATICAL JOURNAL, 2013, 65 (03) : 331 - 339
  • [10] Curvature and topology of compact submanifolds in the unit sphere
    Shu, Shichang
    Liu, Sanyang
    [J]. PACIFIC JOURNAL OF MATHEMATICS, 2006, 228 (02) : 371 - 386
12345