Singularities of null developable of timelike curve that lies on nullcone in semi-Euclidean 3-space with index 2

In this paper, we investigate the null developables of timelike curves that lie on nullcone in 3-dimensional semi-Euclidean space with index 2. We classify the singularities of the null developables of timelike curves. The primary approach is based on the classical unfolding theory in singularity theory, which has been extensively applied in studying singularity problems in Euclidean and semi-Euclidean space. The study shows that the differential geometric invariants of timelike curves measured the order of the contact between a timelike curve and a conic CN contained in . Finally, an example is provided to explain our findings.