On the inextensible flow of semi-real quaternionic curves

This thesis consists of four chapters. The first chapter is devoted to the introduction. In the second chapter, basic concepts in the Euclidean and semi Euclidean space are introduced. Moreover, reel quaternion set and semi-reel quaternion set are introduced and defination of quaternionic curve is given. In the third chapter, inextensibe flow of cırve in 3-dimensional Euclidean space and 3-dimensional Minkowski space is examined. Moreover, flow of real quaternionic curve is defined and conditions for an inextensibility is examined. The fourth chapter is the original part of this study. In this chapter, flow of semi-real quaternionic curve is defined. The necessary and sufficient conditionts for inextensible flow are expressed. Finally evolution equations of curvature are given.