Hypersurface Singularities On Pseudo-ball When N-dimensional Gaussian Like Anti De Sitter Space In The Class

We know that Anti de Sitter space (briefly, AdS-space)is the Lorentzian space form with negativecurvature, closely related to the physical. In the theory of relativity people have the division into spacelikespace、lightlike space and timelike space with lightcone. This paper taking into account Anti de Sittern-space from the contact point of view and give the classification of singularities of AdS-pseudosphereGauss image. The first part is the introduction. Mainly introduce the history and the latest research resultsof singularity theory. In§2we give some basic concept and mark of the semi-Euclidean hyperplanehyperplane with index2, while introducing the local differential geometry of timelike hypersurfacesand defining the AdS-pseudosphere Gauss image of timelike hypersurfaces. In§3we give the AdS-pseudosphere height function on timelike hypersurfaces. In§4and§5we interpret the AdS-pseudosphereGauss image as a Legendrian map and introduce the contact with Ads-small pseudohyperboloid. In§6we get the classification of singularities of AdS-pseudosphere Gauss image in3-Space.