Lorentzian Hypersurface In Anti De Sitter N-Space

In this paper,we mainly research the local differential geometry nature of a Lorentzian Hypersurface in Anti de Sitter n-Space, and define the notions of S_t¹Ã—S_s^n-1-valude light-cone Gauss maps and S_t¹Ã—S_s^n-1-valude lightcone height function, also we structure the lightcone pedal surface, prove the relationship between the singularity of the lightcone pedal surface and the singularity of the lightcone Gauss map which offer the theoretical foundation for singularities of the Lorentzian hypersurfaee using Legendrian theory in future.