Some new associated curves of a Frenet curve in E3 and E4

Authors : Nesibe MACİT, Mustafa DÜLDÜL

Pages : 1023-1037

Doi:10.3906/mat-1401-85

View : 10 | Download : 7

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, firstly, we define a W -direction curve and W -rectifying curve of a Frenet curve in 3-dimensional Euclidean space E3 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 E3. Later, some new associated curves of a Frenet curve are defined in E4.
Keywords : Frenet curve, associated curve, integral curve, general helices, slant helices, rectifying curve