- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 71 Issue: 2
- Quaternionic Bertrand curves according to type 2-quaternionic frame in $\mathbb{R}^{4}$
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 : 8 | Download : 4
Publication Date : 2022-06-30
Article Type : Research
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