Turkish Journal of Mathematics
DOI
10.3906/mat-1712-34
Abstract
For each Frenet curve $\alpha $ in the Euclidean 3-space $\mathbb{E}^{3}$, there exists a unique unit speed curve $\beta$ tangent to the principal normal vector field of $\alpha $. We simply call this curve $\beta $ the natural mate of $\alpha$. The main purpose of this paper is to prove some relationships between a Frenet curve and its natural mate. In particular, we obtain some necessary and sufficient conditions for the natural mate of a Frenet curve to be a helix, a spherical curve, or a curve of constant curvature. Several applications of our main results are also presented.
Keywords
Rectifying curves, natural mate, spherical curves, conjugate mate, helix, slant helix
First Page
2826
Last Page
2840
Recommended Citation
DESHMUKH, SHARIEF; CHEN, BANG-YEN; and ALGHANEMI, AZEB
(2018)
"Natural mates of Frenet curves in Euclidean 3-space,"
Turkish Journal of Mathematics: Vol. 42:
No.
5, Article 58.
https://doi.org/10.3906/mat-1712-34
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss5/58
