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The Gibbons-Hawking ansatz in generalized Kähler geometry (2009.00778v3)
Published 2 Sep 2020 in math.DG, math-ph, math.CV, and math.MP
Abstract: We derive a local ansatz for generalized K\"ahler surfaces with nondegenerate Poisson structure and a biholomorphic $S1$ 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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