Homotopy Groups, Focal Points and Totally Geodesic Immersions

الأصل · EN

In this paper we consider on a complete Riemannian manifold M an immersed totally geodesic hypersurface existing together with an immersed submanifold N without focal points. No curvature condition is needed. We obtained several connectedness results relating the topologies of M and which depend on the codimension of N.