Directional curves of spherical indicatrix curves

This study consists of 4 parts. In the first chapter, information about the usage areas of curves, combined curves, directional curves, {N, C, W} alternative moving frame is given. In the second chapter, basic information about Frenet deriative formulas and {N, C, W} alternative moving frame of tangent indicatrix and principal indicatrix curves of a unit speed curve are given. In the third chapter, the Frenet apparatus of direction curves of tangent indicatrix curve of the unit speed curve is investigated in terms of {N, C, W} alternative moving frame, in 3-dimensional Euclidean space. Accordingly, general helix, slant helix and C-slant helix characterizations of the curve are given. In fourth chapter, similary, the Frenet apparatus of direction curves of principal normal indicatrix curve of the unit speed curve is obtained in terms of the {N, C, W} frame. Lastly, same characterizations of the this direction curves are determined and exampes are given.