Lotay, JD;
Singer, MA;
Fine, J;
(2017)
The space of hyperkähler metrics on a 4-manifold with boundary.
Forum of Mathematics, Sigma
, 5
(e6)
10.1017/fms.2017.3.
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Abstract
Let X be a compact 4-manifold with boundary. We study the space of hyperk¨ahler triples ω1, ω2, ω3 on X, modulo diffeomorphisms which are the identity on the boundary. We prove that this moduli space is a smooth infinite-dimensional manifold and describe the tangent space in terms of triples of closed anti-self-dual 2-forms. We also explore the corresponding boundary value problem: a hyperk¨ahler triple restricts to a closed framing of the bundle of 2-forms on the boundary; we identify the infinitesimal deformations of this closed framing that can be filled in to hyperk¨ahler deformations of the original triple. Finally we study explicit examples coming from gravitational instantons with isometric actions of SU(2).
| Type: | Article |
|---|---|
| Title: | The space of hyperkähler metrics on a 4-manifold with boundary |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1017/fms.2017.3 |
| Publisher version: | http://dx.doi.org/10.1017/fms.2017.3 |
| Language: | English |
| Additional information: | © The Author(s) 2017. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1542509 |
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