Abstract
Flat Lagrangian minimal surfaces in the Lorentzian complex plane \({\mathbb{C}}^{2}_{1}\) 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 \({\mathbb{C}}^{2}_{1}\) are flat surfaces. In this article, we classify all Lagrangian minimal surfaces in \({\mathbb{C}}^{2}_{1}\) which are free from flat points.
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