Quaternionic normal curves

This thesis consists of four chapters. In the first chapter "Introduction" part has been presented. In the second chapter, terms definitions and theorems which are necessary for Öklid space and Lorentz space are given. In the third part, quaternionic normal curves are studied in Euclidean 3-space and four dimensional Euclidean 4-space. The necessary and sufficient conditions are given for a quaternionic curve to be a quaternionic normal curves in E3 and E4 respectively. In the final chapter, semi-real quaternionic normal curves are studied in four dimensional semi-Euclidean space E24 . Moreover, some characterizations of semi-real quaternionic normal curves are given in terms of their curvature functions. The necessary and sufficient conditions are given for a semi-real quaternionic curve to be a semi-real quaternionic normal curves in E24.