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.
MACİT, NESİBE and DÜLDÜL, MUSTAFA
"Some new associated curves of a Frenet curve in E^3 and E^4,"
Turkish Journal of Mathematics: Vol. 38:
6, Article 7.
Available at: https://journals.tubitak.gov.tr/math/vol38/iss6/7