Homotopy groups, focal points, and totally geodesic immersions
Sergio MendoncaHeudson Mirandola
53C20 (53C42)homotopy groupsfocal pointsimmersions
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 $N$.
Indiana University Mathematics Journal
2013
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10.1512/iumj.2013.62.5097
10.1512/iumj.2013.62.5097
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Indiana Univ. Math. J. 62 (2013) 1075 - 1103
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