%0 Journal Article
%T On submanifolds with tamed second fundamental form
%A G. Pacelli Bessa
%A M. Silvana Costa
%J Mathematics
%D 2008
%I arXiv
%R 10.1017/S0017089509990085
%X We show that a complete submanifold $M$ with tamed second fundamental form in a complete Riemannian manifold $N$ with sectional curvature $K_{N}\leq \kappa \leq 0$ are proper, (compact if $N$ is compact). In addition, if $N$ is Hadamard then $M$ has finite topology. We also show that the fundamental tone is an obstruction for a Riemannian manifold to be realized as submanifold with tamed second fundamental form of a Hadamard manifold with sectional curvature bounded below.
%U http://arxiv.org/abs/0805.0323v1