Smarandache Curves of Spacelike Anti-Salkowski Curve with a Timelike Principal Normal According to Frenet Frame
Süleyman Şenyurt, Kemal Eren
Abstract
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Süleyman Şenyurt, Kemal Eren
Abstract
Open-access reader
In this paper, we investigate the regular Smarandache curves obtained from the Frenet vectors of spacelike anti-Salkowski curve with a timelike principal normal. Firstly, we define Smarandache curves depending upon the anti-Salkowski curve. Later, the curvature and the torsion Frenet vectors of Smarandache curves are calculated. Finally, the Frenet apparatuses of the obtained Smarandache curves are expressed as Frenet vectors of the spacelike anti-Salkowski curve. We draw graphic of the obtained Smarandache curves and some related results are given.
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In this paper, we investigate the regular Smarandache curves obtained from the Frenet vectors of spacelike anti-Salkowski curve with a timelike principal normal. Firstly, we define Smarandache curves depending upon the anti-Salkowski curve. Later, the curvature and the torsion Frenet vectors of Smarandache curves are calculated. Finally, the Frenet apparatuses of the obtained Smarandache curves are expressed as Frenet vectors of the spacelike anti-Salkowski curve. We draw graphic of the obtained Smarandache curves and some related results are given.
Key concepts: Frenet–Serret formulas, Torsion of a curve, Torsion (gastropod), Curvature, Mathematics, Mathematical analysis, Geometry, Principal curvature