Classification of Surfaces of Coordinate Finite Type in the Lorentz–Minkowski 3-Space
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CitationAl-Zoubi, H., Akbay, A.K., Hamadneh, T., Al-Sabbagh, M. (2022). Classification of Surfaces of Coordinate Finite Type in the Lorentz–Minkowski 3-Space. Axioms, 11 (7), art. no. 326. https://doi.org/10.3390/axioms11070326
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 ∆I I I x = Ax, where ∆I I I 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.