Uniformization and the Poincare metric on the leaves of a foliation by curves

In this paper we prove that a holomorphic foliation by curves, on a complex compact manifold M, whose singularities are non degenerated and whose tangent line bundle admits a metric of negative curvature, satisfies the following properties: (a): All leaves are hyperbolic. (b): The Poincare metric on the leaves is continuous. (c): The set of uniformizations of the leaves by the Poincare disc IID is normal. Moreover, if (alpha (n))(n greater than or equal to1) is a sequence of uniformizations which converges to a map alpha: D -->M, then either alpha is a constant map (a singularity), or at is an uniformization of some leaf. This result generalizes Theorem B of [LN], in which we prove the same facts for foliations of degree greater than or equal to 2 on projective spaces.