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Geometry and topology
Some characterization of curves in $\widetilde{\mathbf{SL}_{2}\mathbf{ \mathbb{R} }}$
B. Senoussia, M. Bekkarb a Department of Mathematics, Ecole Normale Supérieure, Mostaganem, Algeria
b Department of Mathematics, Faculty of Sciences, University of Oran, Algeria
Abstract:
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 $\widetilde{\mathbf{SL}_{2}\mathbf{ \mathbb{R} }}$.
Keywords:
$\widetilde{\mathbf{SL}_{2}\mathbf{ \mathbb{R} }}$ geometry, biharmonic curves, general helix, rectifying curve.
Received October 10, 2018, published June 26, 2019
Citation:
B. Senoussi, M. Bekkar, “Some characterization of curves in $\widetilde{\mathbf{SL}_{2}\mathbf{ \mathbb{R} }}$”, Sib. Èlektron. Mat. Izv., 16 (2019), 902–915
Linking options:
https://www.mathnet.ru/eng/semr1102 https://www.mathnet.ru/eng/semr/v16/p902
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Abstract page: | 224 | Full-text PDF : | 139 | References: | 24 |
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