Submanifolds with constant scalar curvature (Q5916177)

Let \(M^n\) be a compact submanifold of \(S^{n+p}(c)\) with constant scalar curvature. In this paper, we prove that if the squared norm \(S\) of the second fundamental form satisfies a certain inequality, then \(M^n\) is a totally umbilic or equality holds and we described all \(M^n\) that satisfy this equality.