Abstract
In this paper we will study special spiral surfaces in the three dimensional Euclidean space and we give some characterization of these surfaces. More specifically, we investigate the Chang-Yau operator acting on the Gauss map of spiral surfaces. We also give some results about canonical vector field of these surfaces, i.e., we study incomperssibility of canonical vector field in two types of spiral surfaces. Moreover, we give some necessary conditions for a spiral surface to be a Weingarten surface. Existence of umbilical point is another problem that we investigate about it for a special case of spiral surfaces of the first type.
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