Geometry of Bäcklund transformations I: generality

Hu, Yuhao

doi:10.1090/tran/7992

Geometry of Bäcklund transformations I: generality
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Trans. Amer. Math. Soc. 373 (2020), 1181-1210 Request permission

Abstract:

Using Élie 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.

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