Characteristics of spherical curves according to the quaternionic frame

This thesis consists of six parts. In the first chapter, general informations about quaternions and quaternionic curves. In the second chapter, definitions of the basic expressions in the theory of curves and surfaces are given. In the third chapter, the definition of spherical curves, the conditions of spherical curves and the characteristics of some curves which can be differentiated are given in Euclidean space. In the fourth chapter, the definitions of the basic expressions in the quaternions theory and the properties of the real quaternions are given. In the fifth chapter quaternionic curves are defined in 3 and 4 dimensional Euclidean space and quaternionic Frenet formulas are given. In addition, formulas between quaternionic curvatures and Frenet derivatives are given. In the sixth chapter, any quaternionic space curves in the and Euclidean spaces and the differential equations giving any uniformity are calculated. In addition, some of the characterizations of these equations are given with respect to the quaternionic frame.