On Submanifolds With Parallel Mobius Second Fundamental Form In S^n+p

In this paper, we study umbilic free submanifolds with parallel Mobius second fun-damental form in Sn+P. Firstly, we find that the squared norm of the Blaschke tensor A has a lower bound for these submanifolds, and we get a classification result when it reaches the lower bound. Secondly, we construct some typical examples on these submani-folds. What’s more, we obtain that parallel Mobius second fundamental form implies that parallel Blaschke tensor and other general properties for these submanifolds.