Construction of a surface pencil with a common special surface curve
Publish place: Journal of Mahani Mathematical Research، Vol: 6، Issue: 2
Publish Year: 1396
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_KJMMRC-6-2_001
تاریخ نمایه سازی: 5 خرداد 1398
Abstract:
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 $leftlangle vec{n} ,vec{W}_{0} rightrangle =text{constant}$. 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.
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Authors
Onur Kaya
Manisa Celal Bayar University
Mehmet Önder
Independent Researcher