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Einstein metrics and magnetic monopoles. (English) Zbl 1180.53051

Hijazi, Oussama (ed.), Géométrie différentielle, physique mathématique, mathématiques et société (I). Volume en l’honneur de Jean Pierre Bourguignon. Paris: Société Mathématique de France (ISBN 978-2-85629-258-7/pbk). Astérisque 321, 5-29 (2008).
The author investigates the geometry of the moduli space of centred magnetic monopoles on hyperbolic three-space. Then, using twistor methods he derives some quaternionic Kähler metrics of positive scalar curvature. For the group \( SU(2) \) these have an orbifold compactification but he shows that this is not the case for \( SU(3) \) .
For the entire collection see [Zbl 1160.53003].
Reviewer: Jan Kurek (Lublin)

MSC:

53C28 Twistor methods in differential geometry
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
51N30 Geometry of classical groups
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