Finslerian Viewpoint to the Rectifying, Normal, and Osculating Curves

Authors : Zehra OZDEMİR, Fatma ATES, Nejat EKMEKÇİ

Pages : 30-38

Doi:10.36890/iejg.993188

View : 11 | Download : 7

Publication Date : 2022-04-30

Article Type : Research Paper

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