Classification of zero mean curvature surfaces of separable type in Lorentz-Minkowski space

Abstract

Consider the Lorentz-Minkowski 3-space L 3 with the metric d x 2 + d y 2 − d z 2 in canonical coordinates ( x , y , z ) . A surface in L 3 is said to be separable if it satisfies an equation of the form f ( x ) + g ( y ) + h ( z ) = 0 for some smooth functions f , g and h defined in open intervals of the real line. In this article we classify all zero mean curvature surfaces of separable type, providing a method of construction of examples.