Singularities of the Darboux ruled surface of a space curve in the pseudo-Galilean space

In this article, we establish the singularity theory in a pseudo-Galilean space , a special case of CayleyKlein spaces. We consider the cases where the Darboux ruled surface in is diffeomorphic to some surfaces in the neighbourhood of a singular point. In addition, we investigate the relationship between singularities of discriminant, bifurcation sets of the function, and geometric invariants of curves in . In this article, we establish the singularity theory in a pseudo-Galilean space , a special case of CayleyKlein spaces. We consider the cases where the Darboux ruled surface in is diffeomorphic to some surfaces in the neighbourhood of a singular point. In addition, we investigate the relationship between singularities of discriminant, bifurcation sets of the function, and geometric invariants of curves in .