Submanifolds with constant scalar curvature in space forms.

Let M be an n-dimensional oriented compact submanifold with constant normalized scalar curvature R ≥ c in the space form Fn+p(c). Denote by H and RicM the mean curvature and the Ricci curvature of M respectively. By applying Cheng-Yau’s self-adjoint operator, we first prove that if M is a hypersurface in a unit sphere, and RicM ≥ (n−2)(1+H2), then M is totally umbilical. Furthermore, we investigate the submanifolds in Fn+p(c) with flat normal bundle satisfying RicM ≥ (n − 2)(c + H2) > 0, and obtain a complete classification theorem. [ABSTRACT FROM AUTHOR]