On pointwise 1-type Gauss map of surfaces in E-1(3) concerning Cheng-Yau operator

In this paper, we study surfaces in 3-dimensional Minkowski space in terms of certain type of their Gauss map. We give several results on these surfaces whose Gauss map G satisfies square G = f (G + C) for a smooth function f and a constant vector C, where square denotes the Cheng-Yau operator. In particular, we obtain classification theorems on the rotational surfaces in E-1(3) with space-like axis of rotation in terms of type of their Gauss map concerning the Cheng-Yau operator.