Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1401-85
Keywords
Frenet curve, associated curve, integral curve, general helices, slant helices, rectifying curve
First Page
1023
Last Page
1037
Recommended Citation
MACİT, N, & DÜLDÜL, M (2014). Some new associated curves of a Frenet curve in E^3 and E^4. Turkish Journal of Mathematics 38 (6): 1023-1037. https://doi.org/10.3906/mat-1401-85
