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The Gibbons–Hawking Ansatz in Generalized Kähler Geometry

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Abstract

We derive a local ansatz for generalized Kähler surfaces with nondegenerate Poisson structure and a biholomorphic \(S^1\) action which generalizes the classic Gibbons–Hawking ansatz for invariant hyperKähler manifolds, and allows for the choice of one arbitrary function. By imposing the generalized Kähler–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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Acknowledgements

The authors are grateful to anonymous referees for useful remarks and suggestions. We would also like to thank Vestislav Apostolov and Connor Mooney for helpful discussions.

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Authors and Affiliations

  1. Rowland Hall, University of California, Irvine, CA, USA

    Jeffrey Streets

  2. Chandler-Ullman Hall, Lehigh University, Bethlehem, PA, USA

    Yury Ustinovskiy

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  1. Jeffrey Streets
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  2. Yury Ustinovskiy
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Communicated by P. Chrusciel.

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Streets, J., Ustinovskiy, Y. The Gibbons–Hawking Ansatz in Generalized Kähler Geometry. Commun. Math. Phys. 391, 707–778 (2022). https://doi.org/10.1007/s00220-022-04329-6

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  • DOI: https://doi.org/10.1007/s00220-022-04329-6

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