Translation Weingarten Surfaces In Three-Dimensional Minkowski Space

We always choose the orthogonal frame to study the curves and the surfaces in Minkowski space. The properties of the surfaces can be described by the Gaussian curvature and the mean curvature, so it is very important to study the Weingarten surfaces. Franki Dillen studied the ruled Weingarten surfaces in 1999 and 2006. My teacher, professor Huili Liu studied the translation surfaces which translate along two spacelike directions and the translation surfaces which translate along the spacelike direction and the timelike direction in 1999. His studies give a classification of the translation surfaces which have constant Gaussian curvature and mean curvature.In this article, we study the translation Weingarten surfaces which translate along the two null directions in the pseudo-orthogonal frame. We mainly give a classification of translation surfaces according the linear relations and the square relations of the Gaussian curvature and the mean curvature.