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In this article, we study the class of surfaces of revolution in the3-dimensional Lorentz-Minkowski space with nonvanishing Gauss curvature whoseposition vector x satisfies the condition {\Delta}IIIx = Ax, where A is asquare matrix of order 3 and {\Delta}III denotes the Laplace operator of thesecond fundamental form III of the surface. We show that such surfaces areeither minimal or pseudospheres of a real or imaginary radius.

Surfaces of coordinate finite type in the Lorentz-Minkowski 3-space