Some new associated curves of a Frenet curve in E-3 and E-4


Macit N. , Düldül M.

TURKISH JOURNAL OF MATHEMATICS, vol.38, pp.1023-1037, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38
  • Publication Date: 2014
  • Doi Number: 10.3906/mat-1401-85
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.1023-1037

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.