Tubular Surfaces Whose Gauss Map N Satisfies $Δ^{II}N = ΛN$

In this paper, we consider tubes in the Euclidean 3-space whose Gauss map N is of coordinate finite II-type, i.e., the position vector N satisfies the relation $Δ^{II}N = ΛN$, where $Δ^{II}$ is the Laplace operator with respect to the second fundamental form I of the surface and $Λ$ is a square matrix of order 3. We show that circular cylinders are the only class of surfaces mentioned above of coordinate finite I-type Gauss map.

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