Some new associated curves of a Frenet curve in $\mathbb{E}^3$ and $\mathbb{E}^4$ | Zendy

Nesibe Macit | Zendy; Mustafa Düldül | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Some new associated curves of a Frenet curve in $\mathbb{E}^3$ and $\mathbb{E}^4$

Author(s) -

Nesibe Macit,

Mustafa Düldül

Publication year - 2014

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1401-85

Subject(s) - frenet–serret formulas , mathematics , mathematical analysis , euclidean geometry , tripling oriented doche–icart–kohel curve , geometry , curvature , elliptic curve , schoof's algorithm , quarter period

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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research