Title: Homotopy groups, focal points, and totally geodesic immersions

Authors: Sergio Mendonca and Heudson Mirandola

Issue: Volume 62 (2013), Issue 4, 1075-1103


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