Quaternionic curves with special quaternionic frames and their characterizations

In this thesis, after the introductoury part which consist the historical background of mathematics and quaternions , basic concepts of quaternions and quaternionic curves are given with a different point of view. Afterwards we have focused on the osculating, rectifying and normal curves. Their definition and characterizations are given in four dimensional Euclidean space. Then with the help of type-2 quaternionic frame in 4- dimensional Euclidean space osculating, rectifying and normal quaternionic curves are defined and their characterizations are calculated.In addition, the lieing conditions in some subspaces for the quaternionic curves using type-2 quaternionic frame are investigated and also classified. Finalpart is on the methodology of the study and finding in thesis. At the same time results are given and suggestions are reported.