Some associated curves according to darboux frame in minkowski 3-space

In this thesis, the definition of a k-direction Darboux curve is given using Darboux vectors of a regular curve lying on a surface in 3-dimensional Minkowski space. In case k vector fields are and , the curvature and torsions of the ζ- and η-directed Darboux curves were obtained in terms of the geodesic curvature κ{g}, the normal curvature κ{n}, and the geodesic torsion τ{g} of the curve lying on the surface. Then, the necessary and sufficient conditions are obtained for the ζ- and η-directional Darboux curves to be a helix and a slant helix.