Linear Weingarten factorable surfaces in isotropic spaces

Abstract

In this paper, we deal with a certain factorable surface in the isotropic 3-space satisfying aK +bH = c, where K is the relative curvature, H the isotropic mean curvature and a, b, c is an element of R. We obtain a complete classification for such surfaces. As a further study, we prove that a certain graph surface with K = H-2 is either a non-isotropic plane or a parabolic sphere.