Geodesic
Quasi-minimal Lorentz surfaces in pseudo-euclidean 4-space with neutral metric
Serdica Mathematical Journal, Tome 46 (2020) no. 2, pp. 151-164.

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A Lorentz surface in the pseudo-Euclidean 4-space with neutral metric is called quasi-minimal if its mean curvature vector is lightlike at each point. We prove that any quasi-minimal Lorentz surface whose Gauss curvature \(K\) and normal curvature \(\varkappa\) satisfy the condition \(K^2 - \varkappa^2 \neq 0\) at every point is determined (up to a rigid motion) by five geometric functions satisfying a system of four partial differential equations.
Keywords: quasi-minimal surface, marginally trapped surface, pseudo-Euclidean 4-space, Fundamental theorem, 53B30, 53A35, 53B25 
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     title = {Quasi-minimal {Lorentz} surfaces in pseudo-euclidean 4-space with neutral metric},
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Milousheva, Velichka; Aleksieva, Yana. Quasi-minimal Lorentz surfaces in pseudo-euclidean 4-space with neutral metric. Serdica Mathematical Journal, Tome 46 (2020) no. 2, pp. 151-164. http://geodesic.mathdoc.fr/item/SMJ2_2020_46_2_a4/