The Frenet Vectors and the Curvatures of Curves $\\mathit{{\\mathbf{N-T^{\\ast }B^{\\ast }}}}$ in $\\mathbf{E}^{3}$

Authors : Şeyda KILIÇOGLU, Süleyman ŞENYURT, Sümeyye GÜR MAZLUM

Pages : 11-18

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Publication Date : 2022-12-30

Article Type : Research Paper

Abstract :In this paper, we describe a new pair of curves where the principal normal vector of a curve $\\beta$ and an vector $R^*$ lying in the rectifian plane of a curve $\\beta^*$ are linearly dependent. We name them the curves $N-T^{\\ast }B^{\\ast }$. And we express the Frenet vectors and the curvatures of the curve $\\beta^*$ in terms of the Frenet vectors and the curvatures of the curve $\\beta$.
Keywords : Frenet frame Curvatures Associated curves, Frenet frame Curvatures Associated curves