A New Quaternion Valued Frame of Curves with an Application
FILOMAT, cilt.35, sa.1, ss.315-330, 2021 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 35 Sayı: 1
- Basım Tarihi: 2021
- Doi Numarası: 10.2298/fil2101315c
- Dergi Adı: FILOMAT
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
- Sayfa Sayıları: ss.315-330
- Anahtar Kelimeler: Quaternionic curve, Quaternionic helix, Frenet formulas
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Ankara Üniversitesi Adresli: Evet
Özet
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.