Quaternionic involute-evolute curve couples

Key words: Euclidean Space, Quaternions, Spatial Quaternionic Curve, Quaternionic Curve, Involute-Evolute Curve Couple, CurveThis thesis consists of five chapters. The first chapter is devoted to the introduction. In the second chapter, basic concepts in the Euclidean space and set of quaternions are introduced. Moreover, the fundamental definitions and theorems are given.In the third chapter, involute-evolute curve couples which are the base of our study in the , Euclidean 3-space are introduced and related theorems are given. In addition this, it is shown that the calculations done in the , Euclidean 3-space can be done in the , Euclidean 4-space.The fourth chapter is the original part of this study. In this chapter, by considering there is a bijective correspondence between a curve in the , Euclidean 3-space and a spatial quaternionic curve in the set of real quaternions and using the properties of quaternions, the characterizations of involute-evolute curve couples are obtained. Moreover, the quaternionic curves are considered while obtaining the characterizations of involute-evolute curve couples for .In the fifth chapter of this thesis, a brief summary of the study is given and a suggestion is proposed for investigations in future.