ON THE GAUSS MAP OF SURFACES OF REVOLUTION WITHOUT PARABOLIC POINTS

Abstract

In this article, we study surfaces of revolution without parabolic points in a Euclidean 3-space whose Gauss map C satisfies the condition Delta(h)G = AG, A is an element of Mat(3,R), where Delta(h) denotes the Laplace operator of the second fundamental form It of the surface and Mat(3, R) the set of 3 x 3-real matrices, and also obtain the complete classification theorem for those In particular, we have a characterization of an ordinary sphere in terms of it.