Singularities of line congruences

A line congruence is a two-parameter family of lines in R 3 . In this paper we study singularities of line congruences. We show that generic singularities of general line congruences are the same as those of stable mappings between three-dimensional manifolds. Moreover, we also study singularities of normal congruences and equiaffine normal congruences from the viewpoint of the theory of Lagrangian singularities.