- Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Vol: 21 Issue: 2
- On the Quaternionic Focal Curves
On the Quaternionic Focal Curves
Authors : Nurten (bayrak) Gürses, Özcan Bektaş, Salim Yüce
Pages : 357-366
Doi:10.19113/sdufbed.14005
View : 23 | Download : 7
Publication Date : 2017-04-10
Article Type : Other
Abstract :In this study, a brief summary about quaternions and quaternionic curves are firstly presented. Also, the definition of focal curve is given. The focal curve of a smooth curve consists of the centers of its osculating hypersphere. By using this definition and the quaternionic osculating hyperspheres of these curves, the quaternionic focal curves in the spaces $\Q$ and $\Q_\nu$ with index $\nu=\{1,2\}$ are discussed. Some relations about spatial semi-real quaternionic curves and semi-real quaternionic curves are examined by using focal curvatures and "scalar Frenet equations" between the focal curvatures. Then, the notions: such as vertex, flattenings, a symmetry point are defined for these curves. Moreover, the relation between the Frenet apparatus of a quaternionic curve and the Frenet apparatus of its quaternionic focal curve are presented.Keywords : Quaternions, Quaternionic curves, Osculating hypersphere, Focal curves, Semi-Euclidean space