TY  - JOUR
TT  - On the Quaternionic Focal Curves
AU  - (bayrak) Gürses, Nurten
AU  - Bektaş, Özcan
AU  - Yüce, Salim
PY  - 2017
DA  - August
DO  - 10.19113/sdufbed.14005
JF  - Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi
JO  - J. Nat. Appl. Sci.
PB  - Süleyman Demirel Üniversitesi
WT  - DergiPark
SN  - 1308-6529
SP  - 357
EP  - 366
VL  - 21
IS  - 2
KW  - Quaternions
KW  - Quaternionic curves; Osculating hypersphere; Focal curves; Semi-Euclidean space
N2  - 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.
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UR  - https://doi.org/10.19113/sdufbed.14005
L1  - https://dergipark.org.tr/tr/download/article-file/409380
ER  -