Classification of Surfaces of Coordinate Finite Type in the Lorentz–Minkowski 3-Space

Abstract

In this paper, we define surfaces of revolution without parabolic points in three-dimensional Lorentz–Minkowski space. Then, we classify this class of surfaces under the condition ΔIIIx=Ax, where ΔIII is the Laplace operator regarding the third fundamental form, and A is a real square matrix of order 3. We prove that such surfaces are either catenoids or surfaces of Enneper, or pseudo spheres or hyperbolic spaces centered at the origin.