Translation Surfaces In Three-Dimensional Minkowski Space

Two hundred years ago, Euclidean space, which can reflect the real world to some extents, has been thought the only right space. Man knew little about Non-Euclidean space. At the beginning of the nineteenth century, mathematicians found the reasonability of the pseudo-Euclidean space. After that, pseudo-Euclidean space has become an important topic. The three-dimensional Minkowski space is researched widely.There are two frames which are the orthogonal frame and the pseudo-orthogonal frame in the pseudo-Euclidean space. We can choose the proper frame to study the curves and surfaces.In this article, we choose the pseudo-orthogonal frame to study the translation surfaces which translate along the spacelike and the lightlike directions. We mainly discuss the properties of the translation surfaces whose Gauss curvature and mean curvature satisfy some certain relations.