Rectifying curves in De Sitter 3-space

In this thesis, we give the notion of non-degenerate rectifying curve and non-degenerate conical surface in De Sitter 3-space which is known that Lorentzian space form with positive constant curvature one. Especially, in this thesis for the first time, some characterizations of timelike rectifying curves with nonzero geodesic torsion are obtained in De Sitter 3-space. In this sense, we give relationship between timelike rectifying curve and geodesic of timelike conical surface in De Sitter 3-space. After, we obtain a nice characterization with respect to the ratio of geodesic torsion and geodesic curvature for timelike rectifying curves in De Sitter 3-space. Moreover, we have a characterization which determines all timelike rectifying curve in De Sitter 3-space. Finally, in viewpoint of extremal curves, we give a corollary that a timelike curve in De Sitter 3-space, which has non-zero constant geodesic curvature and linear form geodesic torsion, cong- ruent to a timelike rectifying curve, which is generated by a spiral type unit speed timelike curve with certain geodesic curvature in 2-dimensional pseudo-sphere, and vice versa.