In this paper, by making use of uniqueness polynomials for meromorphic
functions, we obtain a class of uniqueness polynomials for holomorphic
curves from the complex plane into complex projective space. The related
uniqueness problems are also considered.
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.
In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.