Singularities of plane congruences

Igor Chagas, UFBA

Abstract:

In this talk, we study plane congruences from the singularity theory viewpoint. We classify singularities of affine normal plane congruences associated to locally strictly convex surfaces in $\mathbb{R}^4$. We also discuss singularities associated to the affine distance functions and how these singularities are related to the geometry of the surface.