Complete conical type end immersed manifolds in ℝ^N

Jaime Ripoll

Vol. 185 (1998), No. 1, 183–200

DOI: 10.2140/pjm.1998.185.183

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.

Milestones

Received: 30 April 1996

Revised: 12 August 1997

Published: 1 September 1998