On developable ruled surfaces of the principle-direction curve

Abstract

This study is devoted to improve the theory of the developable ruled surfaces in terms of principal-direction curves of any spatial curve in three-dimensional Euclidean space. We obtain the new representation for developable surfaces by slant helices and the useful elements such as pitch, angle of pitch and dral with the help of a new frame {N, C, W}. Furthermore, the investigation is observed under some special cases in terms of the director vector of surface.