On submanifolds of Hopf manifolds

The main results we obtain are as follows: an invariant submanifold of a Hopf manifold with semi-flat normal connection is either a complex hypersurface or a totally-umbilical quasi-Einstein submanifold with a flat normal connection. The only totally-umbilical invariant submanifolds of zero scalar curvature of a Hopf manifold are the totally-geodesic flat surfaces. To Professor A. Cossu on the Occasion of his 65th Birthday