Holomorphic foliations and the Kobayashi metric

T. Duchamp, M. Kalka
1977 Proceedings of the American Mathematical Society  
Here we extend the notion of the Kobayashi metric from complex manifolds to holomorphic foliations of smooth manifolds. This gives a notion of a hyperbolic foliation. We prove that a hyperbolic foliation of a compact manifold is compact and Hausdorff.
doi:10.1090/s0002-9939-1977-0464258-2 fatcat:mowgks3vsfbarains6x4scelg4