Uniqueness among scalar-flat Kähler metrics on non-compact toric 4-manifolds. (English) Zbl 1471.53061
Asymptotically locally Euclidean (ALE for short) describes a four-dimensional Riemannian manifold with just one end which at infinity looks like the quotient space \(\mathbb R^4/\Gamma\) where \(\Gamma\) is a finite group. Donaldson generalised Taub-NUT metrics are all complete scalar-flat Kähler metrics. The author considers \(X=(X,\omega)\), a strictly unbounded sympletic toric four-manifold such that \(J\) is an almost complex structure on \(X\) compatible with \(\omega\), and states that \(\omega(\cdot,J\cdot)\), the associated Riemannian metric on \(X\), is equivariantly isometric to either the ALE toric scalar-flat Kähler metric on \(X\) or to a Donaldson generalised Taub-NUT metric.
Reviewer: Mohammed El Aïdi (Bogotá)
MSC:
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
| 53D20 | Momentum maps; symplectic reduction |
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