Some new associated curves of a Frenet curve in E 3 and E 4

Abstract

In this paper, firstly, we define a W -direction curve and W -rectifying curve of a Frenet curve in 3-dimensional Euclidean space E 3 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 E 3 . Later, some new associated curves of a Frenet curve are defined in E 4 .