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 Finslerianspherical 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 metricand their visualizations are given by using the Mathematica program.