Singular hyperbolic monopoles. (English) Zbl 1134.53013
The twistor theory of singular hyperbolic SU(2) monopoles [Hyperbolic version of Kronheimer’s work on monopoles and Taub-NUT metrics, Transfer Thesis, Oxford University (1985)] is developed. It is shown that the moduli space of charge 1 monopoles possesses a natural 2-sphere of scalar flat Kähler metrics. In the zero mass limit, the metrics reduce to a class of LeBrun metrics.
See also N. J. Hitchin [Math. Proc. Camb. Philos. Soc. 85, 465–476 (1979; Zbl 0405.53016), Commun. Math. Phys. 83, 579–602 (1982; Zbl 0502.58017)]; N. P. Buchdahl [J. Differ. Geom. 24, 19–52 (1986; Zbl 0586.32034)].
See also N. J. Hitchin [Math. Proc. Camb. Philos. Soc. 85, 465–476 (1979; Zbl 0405.53016), Commun. Math. Phys. 83, 579–602 (1982; Zbl 0502.58017)]; N. P. Buchdahl [J. Differ. Geom. 24, 19–52 (1986; Zbl 0586.32034)].
Reviewer: Maido Rahula (Tartu)
MSC:
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 53C28 | Twistor methods in differential geometry |
| 32Q15 | Kähler manifolds |
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