@article{article_382565, title={On the Quaternionic Focal Curves}, journal={Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi}, volume={21}, pages={357–366}, year={2017}, DOI={10.19113/sdufbed.14005}, author={(bayrak) Gürses, Nurten and Bektaş, Özcan and Yüce, Salim}, keywords={Quaternions,Quaternionic curves; Osculating hypersphere; Focal curves; Semi-Euclidean space}, 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.}, number={2}, publisher={Süleyman Demirel University}