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

In this article, we study the class of surfaces of revolution in the 3-dimensional Lorentz-Minkowski space with nonvanishing Gauss curvature whose position vector x satisfies the condition ΔIIIx = Ax, where A is a square matrix of order 3 and ΔIII denotes the Laplace operator of the second fundamental form III of the surface. We show that such surfaces are either minimal or pseudospheres of a real or imaginary radius.

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