Local Differential Geometry On Timelike Surfaces In Anti De Sitter 3-space

In this paper,we mainly research the local differential geometry nature of a timelike surface in Anti de Sitter 3-Space, and define the notions of S_t~1×S_s~1-valude light- cone Gauss maps and S_t~1×S_s~1-valude lightcone height function, prove the relationship between the singularity of thelight- cone Gauss maps and the singularity of the lightcone height function which offer the theoretical foundation for singularities of the timelike surface using Legendrian theory in future.