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.

arXiv comment61 pages, 3 figures, the version to appear in Communications in Mathematical Physics

References in corpus (2)

• Instantons, Poisson structures and generalized Kaehler geometry
• Generalized Kahler Geometry and the Pluriclosed Flow

Cited by in corpus (5)

• The Heterotic-Ricci flow and its three-dimensional solitons
• 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