Tubes in the Euclidean 3-space with coordinate finite type Gauss map

In this paper, we continue the classification of coordinate finite type Gauss map surfaces in the 3-dimensional Euclidean space ${\mathbb{E}^3}$. To do this, we investigate an important family of surfaces, namely, tubes in ${\mathbb{E}^3}$ of which its Gauss map N satisfies the condition ∆IIN= AN, where A ∈ ℝ3×3 and ∆II is the Laplace-Beltrami operator corresponding to the 2nd fundamental form II of the surface. We show that there is no such surfaces satisfying this property.