  De Sitter space is a non-flat Lorentzian space form with positive constant
curvature which plays an important role in the theory of relativity. In this
paper, we define the notions of timelike rectifying curve and timelike conical
surface in De Sitter 3-space as Lorentzian viewpoint. Moreover, we give some
nice characterizations and results of a timelike rectifying curves with respect
to curve-hypersurface frame in De Sitter 3-space which is a three dimensional
pseudo-sphere in Minkowski 4-space.
