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arXiv · 2009.00778

The Gibbons-Hawking ansatz in generalized K\"ahler geometry

Jeffrey Streets·Yury Ustinovskiy
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Abstract

We derive a local ansatz for generalized K\"ahler surfaces with nondegenerate Poisson structure and a biholomorphic $S^1$ 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.

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BibTeXRIS

Jeffrey Streets, Yury Ustinovskiy. 2020-09-02. The Gibbons-Hawking ansatz in generalized K\"ahler geometry. https://doi.org/10.1007/s00220-022-04329-6

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