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On the Quaternionic Focal Curves

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dc.creator (BAYRAK) GÜRSES, Nurten
dc.creator BEKTAŞ, Özcan
dc.creator YÜCE, Salim
dc.date 2017-06-13T00:00:00Z
dc.date.accessioned 2019-07-09T11:58:44Z
dc.date.available 2019-07-09T11:58:44Z
dc.identifier http://dergipark.org.tr/sdufenbed/issue/34634/382565
dc.identifier 10.19113/sdufbed.14005
dc.identifier.uri http://acikerisim.sdu.edu.tr/xmlui/handle/123456789/45945
dc.description 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.
dc.format application/pdf
dc.publisher Süleyman Demirel University
dc.publisher Süleyman Demirel Üniversitesi
dc.relation http://dergipark.org.tr/download/article-file/409380
dc.source Volume: 21, Issue: 2 357-366 en-US
dc.source 1308-6529
dc.subject Quaternions,Quaternionic curves; Osculating hypersphere; Focal curves; Semi-Euclidean space
dc.title On the Quaternionic Focal Curves en-US
dc.type info:eu-repo/semantics/article


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