Submanifolds with constant scalar curvature in space forms

Let Formula: see text be an Formula: see text-dimensional oriented compact submanifold with constant normalized scalar curvature Formula: see text in the space form Formula: see text. Denote by Formula: see text and Formula: see text the mean curvature and the Ricci curvature of Formula: see text respectively. By applying Cheng-Yau’s self-adjoint operator, we first prove that if Formula: see text is a hypersurface in a unit sphere, and Formula: see text, then Formula: see text is totally umbilical. Furthermore, we investigate the submanifolds in Formula: see text with flat normal bundle satisfying Formula: see text, and obtain a complete classification theorem.