A rigidity theorem for non-negatively immersed submanifolds (Q1175578)

Let \(M\) be an \(n\)-dimensional compact submanifold with nonnegative sectional curvature of an \((n+p)\)-dimensional Riemannian manifold of constant sectional curvature. In this paper, the author gives some sufficient conditions for \(M\) to be a Riemannian product of totally umbilical submanifolds. The conditions are given by some function relation with respect to the mean curvature and the scalar curvature. As a special case, a compact surface of a 3-dimensional manifold of constant curvature is also discussed.