Construction of a surface pencil with a common special surface curve
Onur
Kaya
Manisa Celal Bayar University
author
Mehmet
Önder
Independent Researcher
author
text
article
2017
eng
In this study, we introduce a new type of surface curves called $D$-type curve. This curve is defined by the property that the unit Darboux vector $\vec{W}_{0} $ of a surface curve $\vec{r}(s)$ and unit surface normal $\vec{n} $ along the curve $\vec{r}(s)$ satisfy the condition $\left\langle \vec{n} ,\vec{W}_{0} \right\rangle =\text{constant}$. We point out that a $D$-type curve is a geodesic curve or an asymptotic curve in some special cases. Then, by using the Frenet vectors and parametric representation of a surface pencil as a linear combination of the Frenet vectors, we investigate necessary and sufficient condition for a curve to be a $D$-type curve on a surface pencil. Moreover, we introduce some corollaries by considering the $D$-type curve as a helix, a Salkowski curve or a planar curve. Finally, we give some examples for the obtained results.
Journal of Mahani Mathematical Research Center
Shahid Bahonar University of Kerman
2251-7952
6
v.
2
no.
2017
57
72
http://jmmrc.uk.ac.ir/article_1866_f228056f4057aee18d10d5b8fc41f15a.pdf
dx.doi.org/10.22103/jmmrc.2017.10079.1038