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.

Keywords:

Isotropic space, affine factorable surface, mean curvature, Gaussian curvature.