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

B. Senoussi ; M. Bekkar

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 902-915.

Résumé

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 $\widetilde{\mathbf{SL}_{2}\mathbf{ \mathbb{R} }}$.

Détail

Keywords: $\widetilde{\mathbf{SL}_{2}\mathbf{ \mathbb{R} }}$ geometry, biharmonic curves, general helix, rectifying curve.

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