Hyperbolicity of the complement of arrangements of non complex lines

Abstract

The goal of this paper is twofold. We study holomorphic curves $f:\C\longrightarrow \C^3$ avoiding four complex hyperplanes and a real subspace of real dimension five in $\C^3$ where we study the cases where the projection of $f$ into the complex projective space $\C P^2$ is constant. On the other hand, we investigate the kobayashi hyperbolicity of the complement of five perturbed lines in $\C P^2$.