Hokkaido University Preprint Series in Mathematics
A line congruence is a two parameter family of lines in IR3. 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 view point of the theory of Lagrangian singularities.