On the Differential Geometric Elements of the Involute D-Scroll in E-3

Abstract

Deriving curves based on the other curves is a subject in geometry. Involute-evolute curves, Bertrand curves are this kind of curves. By using the similiar method we produce a new ruled surface based on the other ruled surface. In [14], D-scroll, which is known as the rectifying developable surface, of any curve and the involute D-scroll of the curve alpha are alreadyDefined, E-3. In this paper, we consider these special ruled surfaces D-scroll and involute D-scroll, associated to a space curve with curvature k(1) not equal 0 and involute beta. We will examine theDifferential geometric elements (such as, Weingarten map S, curvatures K and H) of the involute D-scroll and D-scroll relative to each other. Further we will examined the fundamental forms too.