  In this paper, we firstly investigate some relations regarding the first and
the second Laplace operators corresponding to the third fundamental form III of
a surface in the Euclidean space E3. Besides, we introduce the finite Chen type
surfaces of revolution with nonvanishing Gauss curvature with respect to the
third fundamental form. We present a special case of this family of surfaces of
revolution in E3, namely, surfaces of revolution with R is constant, where R
denotes the sum of the radii of the principal curvature of a surface.
