Canal Surface Whose Center Curve is a Hyperbolic Curve with Hyperbolic Frame

Authors : Ali UÇUM

Pages : 106-120

Doi:10.36890/iejg.829766

View : 7 | Download : 7

Publication Date : 2021-04-15

Article Type : Research Paper

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 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, $\leftinsert ignore into journalissuearticles values( X,Y\right); $-Weingarten surface and linear Weingarten surface.
Keywords : Canal surfaces, tubular surfaces, hyperbolic curve, Weingarten surface X, Y, Weingarten surface