Quaternionic Bertrand curves according to type 2-quaternionic frame in $\mathbb{R}^{4}$

Abstract

In this paper, we give some characterization of quaternionic Bertrand curves whose the torsion is non-zero but bitorsion is zero in $\mathbb{R}^{4}$ according to Type 2-Quaternionic Frame. One of the most important points in working on quaternionic curves is that given a curve in $\mathbb{R}^{4}$, the curve in $\mathbb{R}^{3}$ associated with this curve is determined individually. So, we obtain some relationships between quaternionic Bertrand curve $\alpha^{(4)}$ in $\mathbb{R}^{4}$ and its associated spatial quaternionic curve $\alpha$ in $\mathbb{R}^{3}$. Also, we support some theorems in the paper by means of an example.

Keywords

• Quaternions
• quaternionic frame
• Bertrand curve
• Euclidean space

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