Hyperbolicity of a complex manifold and other equivalent properties

Abstract

Defining the notions of Schottky, Landau and Picard properties on a plane domain, the first author [3] proved that a domain in C {\mathbf {C}} having any of these properties is equivalent to the hyperbolicity of the domain. In this paper the authors extend these notions to higher-dimensional case and obtain other various equivalent conditions for the hyperbolicity of a complex manifold.