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arXiv · 1301.0621

Einstein--Weyl geometry, dispersionless Hirota equation and Veronese webs

Maciej Dunajski·Wojciech Krynski
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Abstract

We exploit the correspondence between the three-dimensional Lorentzian Einstein-Weyl geometries of the hyper-CR type, and the Veronese webs to show that the former structures are locally given in terms of solutions to the dispersionless Hirota equation. We also demonstrate how to construct hyper-CR Einstein--Weyl structures by Kodaira deformations of the flat twistor space $T\CP^1$, and how to recover the pencil of Poisson structures in five dimensions illustrating the method by an example of the Veronese web on the Heisenberg group.

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Maciej Dunajski, Wojciech Krynski. 2014-01-17. Einstein--Weyl geometry, dispersionless Hirota equation and Veronese webs. https://doi.org/10.1017/s0305004114000164

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