Characterizations of Bertrand Curves in Finsler 3-Manifold

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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