Null surfaces of null curves on 3-null cone

The null surfaces of null curves on 3-null cone have the applications in the studying of horizon types. Via the pseudo-scalar product and Frenet equations, the differential geometry of null curves on 3-null cone is obtained. In the local sense, the curvature describes the contact of submanifolds with pseudo-spheres. We introduce the geometric properties of the curvatures and show the singularities of null surfaces, which are constructed over the null curves.