The Generalization of Helices

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.

Keywords:

clad helices , Slant helices , gauss map , spherical involute , Developable surface