Hyperbolicity of the complement of arrangements of non complex lines

Abstract

The goal of this paper is twofold. We study holomorphic curves f:C ? C3 avoiding four complex hyperplanes and a real subspace of real dimension five in C3 where we study the cases where the projection of f into the complex projective space CP2 is constant. On the other hand, we investigate the kobayashi hyperbolicity of the complement of five perturbed lines in CP2.