Linear Weingarten factorable surfaces in isotropic spaces

Abstract

In this paper, we deal with the linear Weingarten factorable
surfaces in the isotropic 3-space I^{3} satisfying the relation aK +bH = c;
where K is the relative curvature and H the isotropic mean curvature,
a,b,c R. We obtain a complete classication for such surfaces in I^{3}: As
a further study, we classify all graph surfaces in I^{3} satisfying the relation
K = H^{2}; which is the equality case of the famous Euler inequality for surfaces in a Euclidean space.