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

Authors : Ferdağ KAHRAMAN AKSOYAK

Pages : 395-406

Doi:10.31801/cfsuasmas.991631

View : 10 | Download : 13

Publication Date : 2022-06-30

Article Type : Research Paper

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 $\alpha^{insert ignore into journalissuearticles values(4);}$ 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