Submanifolds with constant scalar curvature in a space form (Q335437)

The authors consider submanifolds \(M\) immersed with parallel normalized mean curvature vector field in a Riemannian space form \(Q\). They obtain (1) a Simons-type formula for the Laplacian of the second fundamental form \(A\) of \(M\) and (2) an Omori-type maximum principle for an elliptic operator \(\square\) introduced here. Using these results they characterize submanifolds as above which have, moreover, constant normalized scalar curvature.