Classification of Lorentzian surfaces with parallel mean curvature vector in \({\mathbb E}^4_2\) (Q532090)

A surface in the pseudo-Euclidean space \(E^n_s\), with parallel mean curvature vector, has a variety of uses in mathematics and physics. Considerable work is available on the problem of classifying such spacelike surfaces in \(E^n_s\). In this paper, the authors have presented a complete classification of such Lorentzian surfaces in \(E^4_2\). They have proved the existence of twenty-two families of such Lorentzian surfaces. Conversely, they have shown how to recover every such Lorentzian surface of \(E^4_2\).