Fermi-Walker derivative for some related curves

The aim of this study is to state that many curves in differential geometry can be redefined by Fermi-Walker derivative. These definitions are important in terms of their benefits to geometry. Curves are the most striking subjects in differential geometry. We have introduced a new definition to the W-direction curve by expressing the Fermi-Walker derivative of the W-direction curve defined specifically from these curves. Also, the Fermi-Walker derivative of the Bishop Frame, an alternative approach to the moving frame, was expressed. Thus, the Fermi-Walker parallel frame has been shown to be the Bishop frame, and the Fermi-Walker parallel frame can be used instead of the brake frame. In this thesis, some special characterizations of new associated curves were used with the definition of Fermi-Walker derivative. Keywords: Bishop Frame, Frenet Curves, Fermi-Walker Derivation, W-Direction Curves.