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We introduce null surfaces (or nullcone fronts) of pseudo-spherical spacelikeframed curves in the three-dimensional anti-de Sitter space. These surfaces areformed by the light rays emitted from points on anti-de Sitter spacelike framedcurves. We then classify singularities of the nullcone front of apseudo-spherical spacelike framed curve and show how these singularities arerelated to the singularities of the associated framed curve. We also define afamily of functions called the Anti-de Sitter distance-squared functions toexplain the nullcone front of a pseudo-spherical spacelike framed curve as awavefront from the viewpoint of the Legendrian singularity theory. We finallyprovide some examples to illustrate the results of this paper.

Null surfaces of pseudo-spherical spacelike framed curves in the anti-de Sitter 3-space