Geometry of Bäcklund Transformations I: Generality

Abstract

Using Cartan's Method of Equivalence, we prove an upper bound for the generality of generic rank-1 Bäcklund transformations relating two hyperbolic Monge-Ampère systems. In cases when the Bäcklund transformation admits a symmetry group whose orbits have codimension 1, 2, or 3, we obtain classification results and new examples of auto-Bäcklund transformations.

Proposition 6.6 simplified; minor corrections; 33 pages