数学杂志2022，Vol.42Issue(1)：27-39,13.
Blaschke张量的行列式为常数的2维子流形的研究
STUDY ON 2-DIMENSIONAL SUBMANIFOLDS WITH CONSTANT DETERMINANT OF BLASCHKE TENSOR
余应佳 1郭震1
作者信息
- 1. 云南师范大学数学学院,云南昆明650500
- 折叠
摘要
Abstract
In this paper,we study the rigidity of 2-dimensional submanifolds in S2+p.Let M2 be a 2-dimensional submanifold in the (2 +p)-dimensional unit sphere S2+p without umbilic points.Four basic invariants of M2 under the Moebius transformation group of S2+p are Moebius metric g,Blaschke tensor A,Moebius form Φ and Moebius second fundamental form B.In this paper,by using inequality estimation,we proved the following rigidity theorem:Let x :M2 → S2+p be a 2-dimensional compact submanifold in the (2 + p)-dimensional unit sphere S2+p with vanishing Moebius form Φ and DetA =c(const) ＞ 0,if trA ≥ 1/4,then either x(M2) is Moebius equivalent to a minimal submanifold with constant scalar curvature in S2+p,or S1(r) × S1(√1/1+c2-r2) in S3(1/√1+c2),where r2 =2-√1-64c/ 4(1+c2).Our results complement the case 2-dimensional submanifolds in document[3].关键词
2维子流形/莫比乌斯度量/莫比乌斯形式/莫比乌斯第二基本形式/Blaschke张量Key words
2-dimensional submanifolds/Moebius metric/Moebius form/Moebius second fundamental form/Blaschke tensor分类
数理科学引用本文复制引用
余应佳,郭震..Blaschke张量的行列式为常数的2维子流形的研究[J].数学杂志,2022,42(1):27-39,13.
