Some new associated curves of a Frenet curve in E3 and E4 - Macit, Nesibe; Duldul, Mustafa (Tubitak Scientific & Technological Research Council Turkey, 2014)
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.
Keywords: Frenet curve; associated curve; integral curve; general helices; slant helices; rectifying curve; POSITION VECTOR; SLANT HELIX; Mathematics