We investigate a special timelike surfaces in Anti de Sitter 3-space.We call such a timelike surface an Anti de Sitter horospherical flat surface which belongs to a class of surfaces given by one parameter families of Anti de Sitter horocycle.We give a generic classification of singularities and study the geometric properties of such surfaces from the viewpoint of Legendrian singularity theory.
The weak finite determinacy of relative map-germs is studied. The authors first give the concept of weak finite determination, and then give several sufficient conditions for a relative map-germ to be weak finitely determined, which is an important complement to Mather's work. Moreover, as an application, it is proven that the relative stable map-germs are weak finitely determined.
