Position vectors of curves in the galilean space G$_{3}$

Abstract

In this paper, we study the position vector of an arbitrary curve in Galilean 3-space ${G}_3$. We first determine the positionvector of an arbitrary curve with respect to the Frenet frame. Also, we deduce in terms of the curvature and torsion, the natural representationof the position vector of an arbitrary curve. Moreover, we define a plane curve, helix, general helix, Salkowski curves and anti-Salkowski curves inGalilean space ${G}_3$. Finally, the position vectors of some special curves are obtained and sketching.