GEOMETRY OF BACKLUND TRANSFORMATIONS I: GENERALITY

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