Hyperk\"ahler manifolds with circle actions and the Gibbons-Hawking Ansatz

Mustafa Kalafat; Justin Sawon

Hyperk\"ahler manifolds with circle actions and the Gibbons-Hawking Ansatz

Differential Geometry 2010-09-29 v2 Mathematical Physics math.MP

Authors: Mustafa Kalafat , Justin Sawon

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.

Keywords

hyperkähler manifold circle action Gibbons-Hawking ansatz triholomorphic 4-manifold harmonic function

Cite

@article{arxiv.0910.0672,
  title  = {Hyperk\"ahler manifolds with circle actions and the Gibbons-Hawking Ansatz},
  author = {Mustafa Kalafat and Justin Sawon},
  journal= {arXiv preprint arXiv:0910.0672},
  year   = {2010}
}

Comments

This preprint is withdrawn since it is not ready for public presentation.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

Hyperk\"ahler manifolds with circle actions and the Gibbons-Hawking Ansatz

Abstract

Keywords

Cite

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