Submanifolds of positive Ricci curvature in a Euclidean space

In this paper we study the role of constant vector fields on a Euclidean space Rn+p in shaping the geometry of its compact submanifolds. For an n-dimensional compact submanifold M of the Euclidean space Rn+p with mean curvature vector field H and a constant vector field. on Rn+p, the smooth function phi = < H, xi > is used to obtain a characterization of sphere among compact submanifolds of positive Ricci curvature (cf. main Theorem).