Position vectors of curves with recpect to Darboux frame in the Galilean space G³

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume: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 ŞAHİN, Buket Ceylan DİRİŞEN

Pages : 2079-2093

Doi:10.31801/cfsuasmas.586095

View : 25 | Download : 6

Publication Date : 2019-08-01

Article Type : Research Paper

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

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