【摘要】 本文研究了S^2+p中2维子流形的莫比乌斯刚性问题.设M²是2+p维单位球S^2+p中的无脐子流形,M²在S^2+p的莫比乌斯变换群下的四个莫比乌斯基本量为莫比乌斯度量g,Blaschke张量A,莫比乌斯形式Φ以及莫比乌斯第二基本形式B,利用不等式估计,证明了下列刚性定理:设x:M²→S^2+p是2+p维单位球S^2+p中莫比乌斯形式消失的2维紧致子流形,Blaschke张量A的行列式Det A=c（const）> 0,若tr A≥1/4,那么x（M²）莫比乌斯等价于S^2+p中常曲率极小子流形或者■中环面■,其中■.本文的证明补充了文献[3]中2维子流形情形.更多还原

【Abstract】 In this paper,we study the rigidity of 2-dimensional submanifolds in S^2+p.Let M² be a 2-dimensional submanifold in the（2+p）-dimensional unit sphere S^2+p without umbilic points.Four basic invariants of M² under the Moebius transformation group of S^2+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→S^2+p be a2-dimensional compact submanifold in the（2+p）-dimensional unit sphere S^2+p with vanishing Moebius form Φ and Det A=c（const）> 0,if tr A≥1/4,then either x（M²） is Moebius equivalent to a minimal submanifold with constant scalar curvature in S^2+p,or■ in ■,where ■.Our results complement the case 2-dimensional submanifolds in document [3].更多还原