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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 902–915 (Mi semr1102)  

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.

DOI: https://doi.org/10.33048/semi.2019.16.060

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Bibliographic databases:

UDC: 512.5
MSC: 53B30; 53C40
Received October 10, 2018, published June 26, 2019
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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

Citation in format AMSBIB
\Bibitem{SenBek19}
\by B.~Senoussi, M.~Bekkar
\paper Some characterization of curves in $\widetilde{\mathbf{SL}_{2}\mathbf{ \mathbb{R} }}$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 902--915
\mathnet{http://mi.mathnet.ru/semr1102}
\crossref{https://doi.org/10.33048/semi.2019.16.060}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000473490500001}


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