Study On 2-dimensional Submanifolds With Constant Determinant Of Blaschke Tensor

In this thesis,we study the rigidity of 2-dimensional submanifolds with constant determinant of Blaschke tensor in the(2+p)-dimensional unit sphere 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 ? and Moebius second fundamental form B.In this paper,we prove the following rigidity theorem:Let x:M²? S^2+p be a 2-dimensional compact submanifold in the(2+p)-dimensional unit sphere S^2+p with vanishing Moebius form ? and Det A=c(const)>0,if inf(tr A)?1/4,then either x(M²)is Moebius equivalent to a minimal submanifold with constant scalar curvature in S^2+p,or a torus in S3((?)).