EXTENDED RECTIFYING CURVES AS NEW KIND OF MODIFIED DARBOUX VECTORSY. YAYLI, I. GOK, H.H. HACISALIHOGLU (pp. 18-31)
Rectifying curves are defined as curves whose position vectors always lie in rectifying plane. The centrode of a unit speed curve in E3 with nonzero constant curvature and non-constant torsion (or nonzero constant torsion and non-constant curvature) is a rectifying curve. In this paper, we give some relations between non-helical extended rectifying curves and their Darboux vector fields using any orthonormal frame along the curves. Furthermore, we give some special types of ruled surface. These surfaces are formed by choosing the base curve as one of the integral curves of Frenet vector fields and the director curve as the extended modified Darboux vector fields.
rectifying curve, centrodes, Darboux vector, conical geodesic curvature.