Non-degenerate Submanifolds Of Codimension Two In Anti De Sitter N-space

We study spacelike submanifolds and timelike submanifolds in Anti de Sitter n-space asan application of singularity theory. We define one mapping associated to a spacelike surfacewhich is called a Anti de Sitter nullcone Gauss image. We also define a family of functionsnamed the Anti de Sitter null height function of the spacelike submanifolds. We use this familyof functions as a basic tool to investigate the geometric meanings of singularities of the Anti deSitter nullcone Gauss image. We define one mapping associated to a timelike surface which iscalled a Anti de Sitter null Gauss. We also define a family of functions named the Anti de Sitterhorospherical height function of the timelike submanifolds. We use this family of functions asa basic tool to investigate the geometric meanings of singularities of the Anti de Sitter nullGauss.