Uniqueness among scalar-flat Kähler metrics on non-compact toric $4$-manifolds

Abstract

Abreu-Sena-Dias have constructed two distinct families of scalar-flat Kähler non-compact toric metrics using Donaldson's rephrasing of Joyce's construction in action-angle coordinates. In this paper and using the same set-up, we show that these are the only J-complete scalar-flat Kähler metrics on any given strictly unbounded toric surface. We also show that the asymptotic behaviour of such a metric determines it uniquely.

23 pages

References in corpus (1)

• A generalised Joyce construction for a family of nonlinear partial differential equations

Cited by in corpus (1)

• Invariant scalar-flat Kähler metrics on line bundles over generalized flag varieties