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

TL;DR

This paper classifies certain surfaces in Lorentz-Minkowski 3-space based on a differential equation involving the Laplace operator of the second fundamental form, revealing they are either minimal surfaces or pseudospheres.

Contribution

It provides a complete classification of revolution surfaces with nonvanishing Gauss curvature satisfying a specific Laplace condition in Lorentz-Minkowski space.

Findings

Surfaces are either minimal or pseudospheres.

Classification applies to surfaces with nonvanishing Gauss curvature.

Results extend understanding of surfaces of finite type in Lorentzian geometry.

Abstract

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 {\Delta}IIIx = Ax, where A is a square matrix of order 3 and {\Delta}III 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.