The Characterizations of The Curve Generated by a Curve with Constant Torsion

Year 2023, Volume: 11 Issue: 1, 1 - 7, 30.04.2023

Nural Yüksel Burçin Saltık Murat Kemal Karacan

Abstract

In this article, a curve generated by the curve which has a constant torsion is examined in 3-dimensional Euclidean space. And, the characterizations of this curve have been made and some important theorems have been given. It is seen that the $\overline{\alpha}$ is a curve with constant curvature and the relationships between the two curves $\alpha$ and $\overline{\alpha}$ are revealed. In addition, the conditions for this obtained curve to be helix, slant helix, Bertrand and Salkowski curves are given.

Keywords

constant torsion, Salkowski curve, Bertrand curve, slant helix

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