Characterizations of Bertrand Curves in Finsler 3-Manifold

Year 2020, , 726 - 735, 01.09.2020

Fatma Ateş , Zehra Özdemir , Faik Nejat Ekmekci

https://doi.org/10.35378/gujs.607350

Abstract

In this study, we give the linear condition for the Bertrand curve of a given curve in Finslerian 3-space. Using the Izumiya and Takeuchi’s paper as an inspiration, Bertrand curves of Finslerian spherical curves are defined according to Randers metric which is a special Finslerian metric. Also, we obtain the Finsler helix derived from the Finslerian circle according to Randers metric and their visualizations are given by using the Mathematica program.

Keywords

Finsler space, Randers metric, Indicatrix surface, Bertrand curves, Finsler spherical curve

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