POSITION VECTORS OF CURVES WITH RECPECT TO DARBOUX FRAME IN THE GALILEAN SPACE G3

Abstract

In this paper, we investigate the position vector of a curve on thesurface in the Galilean 3-space G3. Firstly, the position vector of a curve withrespect to the Darboux frame is determined. Secondly, we obtain the standardrepresentation of the position vector of the curve with respect to Darbouxframe in terms of the geodesic, normal curvature and geodesic torsion. As aresult of this, we deÖne the position vectors of geodesic, asymptotic and normalline along with some special curves with respect to Darboux frame. Finally,we elaborate on some examples and provide their graphs.