Geometry of B\"acklund Transformations I: Generality
Differential Geometry
2019-12-03 v2
Abstract
Using Cartan's Method of Equivalence, we prove an upper bound for the generality of generic rank-1 B\"acklund transformations relating two hyperbolic Monge-Amp\`ere systems. In cases when the B\"acklund transformation admits a symmetry group whose orbits have codimension 1, 2, or 3, we obtain classification results and new examples of auto-B\"acklund transformations.
Cite
@article{arxiv.1902.04658,
title = {Geometry of B\"acklund Transformations I: Generality},
author = {Yuhao Hu},
journal= {arXiv preprint arXiv:1902.04658},
year = {2019}
}
Comments
Proposition 6.6 simplified; minor corrections; 33 pages