Metrics and Smooth Uniformisation of Leaves of Holomorphic Foliations
نویسندگان
چکیده
We consider foliations of complex projective manifolds by analytic curves. In a generic case each leaf is hyperbolic and there exists unique Poincaré 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. 2000 Math. Subj. Class. 32Q30 (53C12).
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