# Edge of regression

A type of singularity of differentiable mappings (cf. Singularities of differentiable mappings) of a manifold into a Euclidean space. In the simplest case of a mapping $f$ of a surface $M$ into the three-dimensional Euclidean space $E^3$ an edge of regression represents a smooth curve $L$ in $M$, with smooth image $f(L)\subset E^3$, such that for any $p\in f(L)$ the intersection of $M$ with the plane $\pi$ through $p$ and perpendicular to $f(L)$ is a cusp. It occurs in the pseudo-sphere.

An edge of regression is also called a cuspidal edge. It is the stable caustic of type $A_3$, see [a1], p. 331.