Hyperkähler manifolds with circle actions and the Gibbons-Hawking Ansatz

Abstract

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.

This preprint is withdrawn since it is not ready for public presentation. See also the reference: R.Bielawski, Complete hyper-Kahler 4n-manifolds with a local tri-Hamiltonian Rn-action. Math. Ann. 314 (1999), no. 3, 505-528

References in corpus (1)

• The topology of asymptotically locally flat gravitational instantons

Cited by in corpus (1)

• Scalar-flat Kahler metrics on non-compact symplectic toric 4-manifolds