Rotational Surfaces in Terms of Coordinate Finite Chen II-Type

In this study, we first establish several formulae according to the first and second Beltrami operators. We discuss the class of surfaces of revolution in the 3-dimensional Euclidean space E3 without parabolic points, in which the position vector X satisfies ∆IIX = DX, with ∆II is the Laplace operator of the metric II of the surface and D is a square matrix of order 3. We prove that surfaces satisfying the preceding relation are either part of a sphere or catenoid.