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Construction of a surface pencil with a common special surface curve | ||
| Journal of Mahani Mathematical Research | ||
| مقاله 1، دوره 6، شماره 2، مرداد 2017، صفحه 57-72 اصل مقاله (744.64 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmrc.2017.10079.1038 | ||
| نویسندگان | ||
| Onur Kaya* 1؛ Mehmet Onder2 | ||
| 1Manisa Celal Bayar University, DEPARTMENT OF MATHEMATICS, 45140, MANISA, TURKEY | ||
| 2INDEPENDENT RESEARCHER, DELIBEKIRLI VILLAGE, 31440, KIRIKHAN, HATAY, TURKEY | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Surface pencil؛ $D$-type curve؛ Parametric representation؛ Marching-scale function؛ Surface curve | ||
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آمار تعداد مشاهده مقاله: 563 تعداد دریافت فایل اصل مقاله: 672 |
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