On Invariant Submanifolds of C- and S-Manifolds

We characterize totally geodesic invariant submanifolds of C- and S-manifolds. We prove that the second fundamental form is parallel if and only if the submanifold of an S-manifold is totally geodesic. We show that this is not true for the C-manifolds. This revised version was published online in June 2006 with corrections to the Cover Date.