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. We examine the relationship of the shape operator of a sur-face of Euclidean 3-space with its Gauss map of pointwise 1-type. Sur-faces with constant mean curvature and right circular cones with respectto some properties of the shape operator are characterized when theirGauss map is of pointwise 1-type. 1. IntroductionFor last thirty years or so, the notion of nite type immersions has beenwidely applied in classifying and characterizing the submanifolds in Euclideanspace since it was introduced in the late 1970’s: Let x : M → E m be anisometric immersion of a Riemannian manifold M into the Euclidean space ofdimension m. If we identify x with the position vector at each point p of M, itis a vector valued function. Let ∆ be the Laplacian operator dened on M. Ifx is decomposed as x = x 0 +x 1 +x 2 +··· + x k , it is said to be of nite type,where x 0 is a constant vector and x i non-constant maps satisfying ∆x i = λ i x i for some constant λ i . In particular, if λ i ’s are dierent, we say that it is ofk-type ([3, 4, 15]). It is well known that a submanifold of Euclidean space of1-type is either a minimal submanifold of E

SHAPE OPERATOR AND GAUSS MAP OF POINTWISE 1-TYPE