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arXiv · 1902.04658

Geometry of B\"acklund Transformations I: Generality

Yuhao Hu
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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.

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Yuhao Hu. 2019-02-12. Geometry of B\"acklund Transformations I: Generality. https://doi.org/10.1090/tran/7992

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