Lightlike hypersurfaces along spacelike submanifolds in Minkowski space–time

We consider the singularities of lightlike hypersurfaces along spacelike submanifolds in Lorentz–Minkowski space of general codimension. As an application of the theory of Legendrian singularities, we investigate the geometric meanings of the singularities of lightlike hypersurfaces in terms of the contact of spacelike submanifolds with lightcones.