Quaternionic Bertrand curves according to type 2-quaternionic frame in R4

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.