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

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.