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

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

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