The Generalization of Helices

Abstract

We defined new special curves in Euclidean 3-space which refer to clad helices and found the geometric invariants of clad helices [17]. These notions are generalizations of the notion of cylindrical helices and slant helices. Using the geometric invariants of clad helices in this article, we proposed approaches to construct examples of clad helices in E3 and on S2. Moreover, we obtained the classi cation of special developable surfaces under the condition of the existence of clad helices as a geodesic and existence of slant helices as a line of curvature.