  We describe the space of isometric immersions from the Lorentz plane $L^2$
into the 3-dimensional anti-de Sitter space, and solve several open problems of
this context raised by M. Dajczer and K. Nomizu in 1981. We also obtain from
the above result a description of the space of Lorentzian flat tori
isometrically immersed in the anti de Sitter space in terms of pairs of closed
curves with wave front singularities in the hyperbolic plane satisfying some
compatibility conditions.
