Directional Bertrand Curves

Abstract

It is well known that a characteristic property of the Bertrand curve is

the existence of a linear relation between its curvature and torsion. In this

paper, we propose a new method for generating Bertrand curves, which

avoids the basic restrictions. Our main result is that every space curve is

a directional Bertrand curve with innite directional Bertrand mates.

Keywords

• Bertrand Curves,,offset,,Frenet frame

References

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2. Choi, J.H., Kang, T.H. & Kim, Y.H. 2012. Bertrand curves in 3- dimensional space forms. Applied Mathematics and Computation, 219: 1040-1046.
3. Ekmekci, N. & Ilarslan, K. 2001. On Bertrand curves and their characterization. Differential Geometry Dynamical System, 3: 17-24.