Some remarks on a theorem of Green

Abstract

The purpose of this paper is to study holomorphic curves f from C to C3 avoiding four complex hyperplanes and a real subspace of real dimension four in C3. We show that the projection of f into the complex projective space C P^2 does not remain constant as in the complex case studied by Green, which indicates that the complex structure of the avoided hyperplanes is a necessary condition in the Green theorem

Keywords

• complex manifold
• projective space
• kobayashi hyperbolicity
• holomorphic curves
• holomorphic curves avoiding hyperplane