Classification of Quasi-Minimal Surfaces with Parallel Mean Curvature Vector in Pseudo-Euclidean 4-Space ${\mathbb E}^4_2$

Abstract.

A surface in the pseudo-Euclidean space ${\mathbb E}^4_2$ with neutral metric (or in the Lorentzian complex plane C₁²) is called quasi-minimal if its mean curvature vector is light-like at each point. Such surface are always Lorentzian. In this article, we completely classify quasi-minimal surfaces with parallel mean curvature vector in the pseudo-Euclidean space ${\mathbb E}^4_2$.