Surfaces in E³ with L₁-pointwise 1-type Gauss map

In this paper, we study surfaces in E³ whose Gauss map G satisfies the equation □ G = f(G + C) for a smooth function f and a constant vector C, where □ stands for the Cheng-Yau operator. We focus on surfaces with constant Gaussian curvature, constant mean curvature and constant principal curvature with such a property. We obtain some classification and characterization theorems for these kinds of surfaces. Finally, we give a characterization of surfaces whose Gauss map G satisfies the equation □G = λ(G + C) for a constant λ and a constant vector C.