本文研究了S2+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S2+p中的无脐子流形,M2在S2+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→S2+p是2+p维单位球S2+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DetA=c(const)＞o,若trA≥j,那么x(M2)莫比乌斯等价于S2+p中常曲率极小子流形或者S3(1/√1+c2)中环面S1(r)×S1(√1/1+c2-r2),其中r2=2-√1-64c/4(1+c2)本文的证明补充了文献[3]中2维子流形情形.“,”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].