abstract:A Riemannian submanifold N of a Riemannian manifold M is a submanifold of M equipped with the Riemannian metric inherited from M. The image of an isometric immersion is a Riemannian submanifold.
In this paper, we get a necessary and sufficient condition for a generalcodimensionalsubmanifold with constantmeancurvature in a Riemannian mani-fold to be a totally umbilicalsubmanifold.