Quaternionic (1,3)-Bertrand Curves According to Type 2-Quaternionic Frame in R^4

TL;DR

This paper defines and investigates quaternionic (1,3)-Bertrand curves in R^4 using Type 2-Quaternionic Frames, revealing that such curves must have vanishing torsion or bitorsion, thus extending the understanding of quaternionic curves.

Contribution

It introduces the concept of quaternionic (1,3)-Bertrand curves based on Type 2-Quaternionic Frames and derives new properties, expanding the theory of quaternionic curves in four-dimensional space.

Findings

Quaternionic Bertrand curves have zero torsion or bitorsion.

New characterization of quaternionic (1,3)-Bertrand curves.

Extension of quaternionic curve theory in R^4.

Abstract

If there exists a quaternionic Bertrand curve in E4, then its torsion or bitorsion vanishes. So we can say that there is no quaternionic Bertrand curves whose torsion and bitorsion are non-zero. Hence by using the method which is given by Matsuda and Yorozu [13], we give the definition of quaternionic (1,3)-Bertrand curve according to Type 2-Quaternionic Frame and obtain some results about these curves.