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

Authors : Nural YÜKSEL, Burçin SALTIK, Murat Kemal KARACAN

Pages : 1-7

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Publication Date : 2023-04-30

Article Type : Research Paper

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