Metrics and smooth uniformisation of leaves of holomorphic foliations

We consider foliations of complex projective manifolds by analytic curves. In a generic case each leaf is hyperbolic and there exists unique Poincare metric on the leaves. It is shown that in a generic case this metric smoothly depends on a leaf. The manifold of universal covering of the leaves passing through some transversal base has a natural complex structure. It is shown that this structure can be defined as a smooth almost complex structure on the product of the base and a fiber and there exists a natural pseudoconvex exhaustion.