  We prove several finiteness results for the class $M_{a,b,G,n}$ of
$n$-manifolds that have fundamental groups isomorphic to $G$ and that can be
given complete Riemannian metrics of sectional curvatures within $[a,b]$ where
$a\le b<0$. In particular, if $M$ is a closed negatively curved manifold of
dimension at least three, then only finitely many manifolds in the class
$M_{a,b,\pi_1(M), n}$ are total spaces of vector bundles over $M$. Furthermore,
given a word-hyperbolic group $G$ and an integer $n$ there exists a positive
$\epsilon=\epsilon(n,G)$ such that the tangent bundle of any manifold in the
class $M_{-1-\epsilon, -1, G, n}$ has zero rational Pontrjagin classes.
