Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$

Authors : Sümeyye Gür Mazlum, Süleyman Şenyurt, Mehmet Bektaş

Pages : 12-26

Doi:10.53570/jnt.1140546

View : 25 | Download : 9

Publication Date : 2022-09-30

Article Type : Research

Abstract :In this study, we examine some properties of Salkowski curves in $\mathbb{E}^{3}$. We then make sense of the angle $(nt)$ in the parametric equation of the Salkowski curves. We provide the relationship between this angle and the angle between the binormal vector and the Darboux vector of the Salkowski curves. Through this angle, we obtain the unit vector in the direction of the Darboux vector of the curve. Finally, we calculate the modified orthogonal frames with both the curvature and the torsion and give the relationships between the Frenet frame and the modified orthogonal frames of the curve.
Keywords : Salkowski curve, modified orthogonal frame, Frenet frame