- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 68 Issue: 2
- Position vectors of curves with recpect to Darboux frame in the Galilean space G³
Position vectors of curves with recpect to Darboux frame in the Galilean space G³
Authors : Tevfik Şahin, Buket Ceylan Dirişen
Pages : 2079-2093
Doi:10.31801/cfsuasmas.586095
View : 10 | Download : 7
Publication Date : 2019-08-01
Article Type : Research
Abstract :In this paper, we investigate the position vector of a curve on the surface in the Galilean 3-space G³. Firstly, the position vector of a curve with respect to the Darboux frame is determined. Secondly, we obtain the standard representation of the position vector of the curve with respect to Darboux frame in terms of the geodesic, normal curvature and geodesic torsion. As a result of this, we define the position vectors of geodesic, asymptotic and normal line along with some special curves with respect to Darboux frame. Finally, we elaborate on some examples and provide their graphs.Keywords : Position vector, Darboux frame, geodesic, Galilean 3-space