Finslerian Viewpoint to the Rectifying, Normal, and Osculating Curves

Year 2022, Volume: 15 Issue: 1, 30 - 38, 30.04.2022

Zehra Ozdemir , Fatma Ates , Nejat Ekmekçi

https://doi.org/10.36890/iejg.993188

Abstract

The theory of Finsler metric was introduced by Paul Finsler, in 1918. The author defines this metric using the Minkowski norm instead of the inner product. Therefore, this geometry is a more general metric and includes the Riemannian metric. In the present work, using the Finsler metric, we investigate the position vector of the rectifying, normal and osculating curves in Finslerian 3-space $\mathbb{F}^{3}$. We obtain the general characterizations of these curves in $\mathbb{F}^{3}$. Furthermore, we show that rectifying curves are extremal curves derived from the Finslerian spherical curve. We also plotted various examples by using the Randers metrics.

Keywords

Special curves, Finsler space, Randers metric, centrodes, extremal curves.

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