The Gibbons-Hawking ansatz in generalized Kähler geometry

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.

61 pages, 3 figures, the version to appear in Communications in Mathematical Physics

Cited by in corpus (5)

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• Three-dimensional positively curved generalized Ricci solitons with SO(3)-symmetries
• The stability of non-Kähler Calabi-Yau metrics
• Codimension four regularity of generalized Einstein structures
• Heterotic solitons on four-manifolds