Some characterization of curves in $\widetilde{\mathbf{SL}_{2}\mathbf{ \mathbb{R} }}$

In 1997 Emil Molnár introduced [15] the hyperboloid model of $\widetilde{\mathbf{SL}_{2}\mathbf{ \mathbb{R} }}$ space. In this paper, we obtained characterizations of a curve with respect to the Frenet frame of $\widetilde{\mathbf{SL}_{2}\mathbf{ \mathbb{R} }}$. Rectifying curves are introduced in [3] as space curves whose position vector always lies in its rectifying plane. We characterize rectifying curves in $\widetilde{\mathbf{SL}_{2}\mathbf{ \mathbb{R} }}$.