Abstract

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

Keywords: Position vectors; Frenet equations; Galilean 3-space.

MSC: 53A35, 53B30, 53C50

Pages:  200$-$210     

Volume  64 ,  Issue  3 ,  2012