The Gibbons-Hawking ansatz in generalized K\"ahler geometry
Differential Geometry
2022-02-09 v3 Mathematical Physics
Complex Variables
math.MP
Abstract
We derive a local ansatz for generalized K\"ahler surfaces with nondegenerate Poisson structure and a biholomorphic action which generalizes the classic Gibbons-Hawking ansatz for invariant hyperK\"ahler manifolds, and allows for the choice of one arbitrary function. By imposing the generalized K\"ahler-Ricci soliton equation, or equivalently the equations of type IIB string theory, the construction becomes rigid, and we classify all complete solutions with the smallest possible symmetry group.
Keywords
Cite
@article{arxiv.2009.00778,
title = {The Gibbons-Hawking ansatz in generalized K\"ahler geometry},
author = {Jeffrey Streets and Yury Ustinovskiy},
journal= {arXiv preprint arXiv:2009.00778},
year = {2022}
}
Comments
61 pages, 3 figures, the version to appear in Communications in Mathematical Physics