Some characterization of curves in \(\widetilde{\mathbf{SL}_2\mathbb{R}}\) space. (English) Zbl 1421.53023
Summary: In [Beitr. Algebra Geom. 38, No. 2, 261–288 (1997; Zbl 0889.51021)] E. Molnár introduced the hyperboloid model of \(\widetilde{\mathbf{SL}_2\mathbb{R}}\) space. In this paper, we obtained characterizations of a curve with respect to the Frenet frame of \(\widetilde{\mathbf{SL}_2\mathbb{R}}\). Rectifying curves are introduced as space curves whose position vector always lies in its rectifying plane. We characterize rectifying curves in \(\widetilde{\mathbf{SL}_2\mathbb{R}}\).
MSC:
| 53B25 | Local submanifolds |
| 53B30 | Local differential geometry of Lorentz metrics, indefinite metrics |
Keywords:
\(\widetilde{\mathbf{SL}_2\mathbb{R}}\) geometry; biharmonic curves; general helix; rectifying curveCitations:
Zbl 0889.51021References:
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