On submanifolds with tamed second fundamental form

We show that a complete submanifold $M$ with tamed second fundamental form in a complete Riemannian manifold $N$ with sectional curvature $K_{N}\leq \kappa \leq 0$areproper,(compactif$N$iscompact)\mathrm{.}Inaddition,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.