A New Quaternion Valued Frame of Curves With an Application

Gizem Cansu, Yusuf Yaylı, İsmail Gök

Abstract


The aim of the paper is to obtain a new version of
Serret-Frenet formulae for a quaternionic curve in $\mathbb{R}^4$ by
using the method given by Bharathi and Nagaraj. Then, we define
quaternionic helices in $\mathbb{H}$ named as quaternionic right and
left $X$−helix with the help of given a unit vector field $X$. Since the
quaternion product is not commutative, the authors ([4], [7]) have used
by one-sided multiplication to find a space curve related to a given
quaternionic curve in previous studies. Firstly, we obtain new
expressions by using the right product and the left product for
quaternions. Then, we generalized the construction of Serret-Frenet
formulae of quaternionic curves. Finally, as an application, we obtain
an example that supports the theory of this paper.


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