In this study, we introduce a new type of surface curves called -type curve. This curve is defined by the property that the unit Darboux vector of a surface curve and unit surface normal along the curve satisfy the condition . We point out that a -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 -type curve on a surface pencil. Moreover, we introduce some corollaries by considering the -type curve as a helix, a Salkowski curve or a planar curve. Finally, we give some examples for the obtained results.
Kaya, O. and Onder, M. (2017). Construction of a surface pencil with a common special surface curve. Journal of Mahani Mathematical Research, 6(2), 57-72. doi: 10.22103/jmmrc.2017.10079.1038
MLA
Kaya, O. , and Onder, M. . "Construction of a surface pencil with a common special surface curve", Journal of Mahani Mathematical Research, 6, 2, 2017, 57-72. doi: 10.22103/jmmrc.2017.10079.1038
HARVARD
Kaya, O., Onder, M. (2017). 'Construction of a surface pencil with a common special surface curve', Journal of Mahani Mathematical Research, 6(2), pp. 57-72. doi: 10.22103/jmmrc.2017.10079.1038
CHICAGO
O. Kaya and M. Onder, "Construction of a surface pencil with a common special surface curve," Journal of Mahani Mathematical Research, 6 2 (2017): 57-72, doi: 10.22103/jmmrc.2017.10079.1038
VANCOUVER
Kaya, O., Onder, M. Construction of a surface pencil with a common special surface curve. Journal of Mahani Mathematical Research, 2017; 6(2): 57-72. doi: 10.22103/jmmrc.2017.10079.1038
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