This article is cited in 1 paper

Geometry and topology

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

B. Senoussi^a, M. Bekkar<sup>b

a</sup> 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.

UDC: 512.5

MSC: 53B30; 53C40

Received October 10, 2018, published June 26, 2019

Language: English

DOI: 10.33048/semi.2019.16.060

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