A New Quaternion Valued Frame of Curves with an Application

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Cansu G., YAYLI Y., GÖK İ.

FILOMAT, vol.35, no.1, pp.315-330, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.2298/fil2101315c
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.315-330
  • Keywords: Quaternionic curve, Quaternionic helix, Frenet formulas
  • Ankara University Affiliated: Yes

Abstract

The aim of the paper is to obtain a new version of Serret-Frenet formulae for a quaternionic curve in R-4 by using the method given by Bharathi and Nagaraj. Then, we define quaternionic helices in 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.