Canal surface whose center curve is a hyperbolic curve with hyperbolic frame

Abstract

In this paper, we obtain the parametrization of the canal surfaces whose center curves are the hyperbolic curves on the hyperbolic space H 2 in E 31 . The parametrization of the canal surface is expressed according to the hyperbolic frame given in [10]. Then, the parallel surface of this surface is studied. Also, we define the notion of the associated canal surface. Lastly, we give the geometric properties of these surfaces such that Weingarten surface, ( X, Y ) -Weingarten surface and linear Weingarten surface.