Abstract

We introduce and describe the topology of a family of complete immersed manifolds in R^N, having a nice behaviour at infinity, which we call conical type end manifolds. Our main result states that a complete, non compact immersed manifold in R^N, whose limsup of the norm of the second fundamental form times the intrinsic distance of the manifold to a fixed point is strictly less than 1, as the distance goes to infinity, is a conical type end manifold. In particular, it follows that the manifold has finite topology and is properly immersed in R^N.

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