The S_t～1×S_s～1-valued Lightcone Gauss Map Of A Lorentzian 2-Submanifold In Semi-Euclidean 4-space

We define the notions of S_t~1×S_s~1-valued lightcone Gauss maps , Lorentzian lightcone height function of Lorentzian 2-submanifolds ,Hghtlike hypersurface and distance square function in semi-Euclidean 4-space , established the relationships between singularities of these objects and geometric invariants of the 2-submanifolds as applications of standard techniques of singularity theory for the Lorentzian lightcone height function.