Study On The M?bius Rigidity Of A Class Of Submanifolds In Sphere Space

Suppose M~m is an immersed submanifold in the unit sphere space S~n,on which the Blaschke tensor A is the fundamental Mobius invari-ant.In this thesis,we study the conformal invariants ‖A‖2-(tr A)2 is constant submanifolds Mobius rigidity.We obtain an inequality about the integral of the cubic function of the norm of isotropic Blaschke ten-sor,and classify this class of submanifolds when the equality holds in the inequality.