Affine factorable surfaces of finite type in the 3-dimensional Euclidean E3 and Lorentzian L3 spaces

In this paper we study affine factorable surfaces in the 3- dimensional Euclidean space E 3 and Lorentzian L 3 under the condition ∆ri = λiri, where λi ∈ R and ∆ denotes the Laplace operator with respect to the first fundamental form.