BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.50, no.3, pp.935-949, 2013 (Journal Indexed in SCI)
In this paper, we study surfaces in E-3 whose Gauss map G satisfies the equation square G = f(G + C) for a smooth function f and a constant vector C, where square 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 square G = lambda(G + C) for a constant lambda and a constant vector C.