Pseudo-spherical normal Darboux images of curves on a timelike surface in three dimensional Lorentz–Minkowski space

In this paper we introduce the notion of pseudo-spherical normal Darboux images of curves on a timelike surface in three dimensional Lorentz–Minkowski space. We investigate the singularities and geometric properties of these pseudo-spherical normal Darboux images. Furthermore, we investigate the relation of the de Sitter and of the hyperbolic normal Darboux images of a spacelike curve in S12 with the lightlike surface along this spacelike curve.