Weighted minimal translation surfaces in Minkowski 3-space with density

Abstract

The aim of this work is to study translation surfaces in a Minkowski 3-space [Formula: see text] with density. Translation surfaces in [Formula: see text] are defined as the two generating curves which lie in orthogonal planes. They have actually three different possible parametrizations according to the intersecting straight line of the two planes. We completely classify all translation surfaces with zero weighted mean curvature in [Formula: see text] with density [Formula: see text] by solving the second-order non-linear ODE with some smooth functions.