Einstein--Weyl geometry, dispersionless Hirota equation and Veronese webs
Differential Geometry
2019-02-20 v2 High Energy Physics - Theory
Exactly Solvable and Integrable Systems
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 , 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.
Cite
@article{arxiv.1301.0621,
title = {Einstein--Weyl geometry, dispersionless Hirota equation and Veronese webs},
author = {Maciej Dunajski and Wojciech Krynski},
journal= {arXiv preprint arXiv:1301.0621},
year = {2019}
}
Comments
11 pages. Minor changes. Final version, to appear in the Mathematical Proceedings of the Cambridge Philosophical Society