Lagrangian minimal surfaces in Lorentzian complex plane

摘要

Flat Lagrangian minimal surfaces in the Lorentzian complex plane mathbbC2₁{mathbb{C}}^{2}_{1} are classified by B. Y. Chen and L. Vrancken in [8]. On the other hand, Vrancken proves in [11] that Lagrangian minimal surfaces of constant curvature in mathbbC2₁{mathbb{C}}^{2}_{1} are flat surfaces. In this article, we classify all Lagrangian minimal surfaces in mathbbC2₁{mathbb{C}}^{2}_{1} which are free from flat points.