On the Quaternionic Focal Curves

In this study, a brief summary about quaternions and quaternionic curves arefirstly presented. also, the definition of focal curve is given. the focal curve of a smoothcurve consists of the centers of its osculating hypersphere. by using this definition and thequaternionic osculating hyperspheres of these curves, the quaternionic focal curves in thespaces q and qv with index v = {1;2} are discussed. some relations about spatial semirealquaternionic curves and semi-real quaternionic curves are examined by using focalcurvatures and scalar frenet equations between the focal curvatures. then, the notions:such as vertex, flattenings, a symmetry point are defined for these curves. moreover, therelation between the frenet apparatus of a quaternionic curve and the frenet apparatus ofits quaternionic focal curve are presented.