Kähler–Einstein metrics with SU(2) action

Kähler–Einstein metrics with SU(2) action

The aim of this paper is to analyse Riemannian Kähler–Einstein metrics g in real dimension four admitting an isometric action of SU(2) with generically three-dimensional orbits. The Kähler condition means that there is a complex structure I, with respect to which the metric is hermitian, such that t...

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 1994-05, Vol.115 (3), p.513-525
Hauptverfasser: Dancer, Andrew S., Strachan, Ian A. B.
Format: Artikel
Sprache:eng
Schlagworte:
Differential geometry
Exact sciences and technology
Geometry
Mathematics
Sciences and techniques of general use
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Zusammenfassung:The aim of this paper is to analyse Riemannian Kähler–Einstein metrics g in real dimension four admitting an isometric action of SU(2) with generically three-dimensional orbits. The Kähler condition means that there is a complex structure I, with respect to which the metric is hermitian, such that the two-form Ωdefined by is closed. It is well-known that if this condition holds then Ω is in fact covariant constant.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004100072273