Some new associated curves of a Frenet curve in E³ and E⁴

In this paper, firstly, we define a W -direction curve and W -rectifying curve of a Frenet curve in 3-dimensional Euclidean space E3 by using the unit Darboux vector field W of the Frenet curve and give some characterizations together with the relationships between the curvatures of each associated curve. We also introduce a V -direction curve, which is associated with a curve lying on an oriented surface in E3. Later, some new associated curves of a Frenet curve are defined in E4.