Physical Sciences and Mathematics Commons^™

Some New Associated Curves Of A Frenet Curve In E^3 And E^4, Nesi̇be Maci̇t, Mustafa Düldül

Turkish Journal of Mathematics

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.