Affine Factorable Surfaces in Isotropic Spaces

Abstract

In this paper, we study the problem of finding affine factorable surfaces in a 3-dimensional isotropic space I-3 with prescribed Gaussian (K) or mean (H) curvatures. Because the absolute figure of I-3, by permutation of coordinates two different types of these surfaces appear. We firstly classify the affine factorable surfaces of type 1 with K;H constants. Afterwards, we provide the affine factorable surfaces of type 2 with K = const: or H = 0: Besides in some particular cases, the affine factorable surfaces of type 2 with H = const were obtained.