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 $%\mathbb{E}_{1}^{3}$. The parametrization of the canal surface is expressed according to the hyperbolic frame given in [10]. Then, the parallelsurface of this surface is studied. Also, we define the notion of the associated canal surface. Lastly, we give the geometric properties of thesesurfaces such that Weingarten surface, $\left( X,Y\right) $-Weingarten surface and linear Weingarten surface.