On the evolution of semi real qaterniyonic curves in the semi Euclidean space E42

This study consists of four parts. The first chapter includes the introduction. In the second part, basic concepts in Euclidean space and semi-Euclidean space are given. In addition, the basic concepts in the set of real quaternions and semi-real quaternions are given, and real quaternionic curves and semi-real quaternionic curves are mentioned. In the third chapter, the inextensible flow of curve in n-dimensional Euclidean space and 3-dimensional Minkowski space has been investigated. In addition, in this section, the inextensible flow of real quaternionic curve has been examined, the evolution equations related to the Frenet frame and curvatures of the quaternionic curve have been obtained, and the condition of integration has been provided by using the curve flow. The fourth part is the original part of this study. In this section, inextensible flow of semi-real quaternionic curves have been investigated. The evolution equations related to the Frenet frame and curvatures of the semi-real quaternionic curve flow is given. Finally, examples related to the evolution equations of curvatures are given.