Associated curves of a frenet curve and their applications

This thesis consists of seven sections. In the first section literature summary and the purpose of the thesis are given. The second section includes some basic concepts of the curves and surfaces. In the third section, the definitions of associated curves of a Frenet curve and their various characterizations with applications are introduced. The fourth, fifth and sixth sections are original part of the thesis. In the fourth section, the involutes and the tangential indicatrix of principal-direction curve are investigated. Later, direction curve and rectifying curve are defined and some characterizations of these curves are given. In the fifth section, direction curve is defined for a curve that lies on a surface and by examining the relationship between curvatures of these associated curves, some examples are given. In the sixth section, the definitions of principal-direction curve, direction curve, direction curve and rectifying curve are defined in and some characterizations of these curves are obtained. Seventh section consists of conclusions and suggestions.