Some Special Ruled Surfaces Generated by a Direction Curve according to the Darboux Frame and their Characterizations - Nidal Echabbi; Amina Ouazzani Chahdi (Abstract and Applied Analysis)
In this work, we consider the Darboux frame T,V,U of a curve lying on an arbitrary regular surface and we construct ruled surfaces having a base curve which is a V-direction curve. Subsequently, a detailed study of these surfaces is made in the case where the directing vector of their generatrices is a vector of the Darboux frame, a Darboux vector field. Finally, we give some examples for special curves such as the asymptotic line, geodesic curve, and principal line, with illustrations of the different cases studied.