Some properties of surfaces of finite III-type

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 E. 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 E, namely, surfaces of revolution with R is constant, where R denotes the sum of the radii of the principal curvature of a surface. Key-Words: Surfaces in the Euclidean 3-space, Surfaces of finite Chen-type, Laplace operator, Surfaces of revolution.

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