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In this paper, we consider tubes in the Euclidean 3-space whose Gauss map Nis of coordinate finite II-type, i.e., the position vector N satisfies therelation $\Delta^{II}N = \Lambda N$, where $\Delta^{II}$ is the Laplaceoperator with respect to the second fundamental form I of the surface and$\Lambda$ is a square matrix of order 3. We show that circular cylinders arethe only class of surfaces mentioned above of coordinate finite I-type Gaussmap.

Tubular Surfaces Whose Gauss Map N Satisfies $\Delta^{II}N = \Lambda N$