Hyperk\"ahler manifolds with circle actions and the Gibbons-Hawking Ansatz
classification
🧮 math.DG
math-phmath.MP
keywords
ansatzcirclegibbons-hawkingactionactionsahlercompletefunction
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We show that a complete simply-connected hyperkaehler 4-manifold with an isometric triholomorphic circle action is obtained from the Gibbons-Hawking ansatz with some suitable harmonic function.
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