Gravitational instantons with faster than quadratic curvature decay (III)

Abstract

This is our third paper in a series on the gravitational instantons. In this paper, we classify ALG and ALH gravitational instantons. In ALG case, we extend Hein's construction slightly and show that it's the only ALG gravitational instanton. In ALH case, we prove a Torelli-type theorem.

In the ALG-II^*,III^*,IV^* cases, we add the classification result and a counterexample of the Torelli theorem

References in corpus (2)

• Symplectic Manifolds and Isomonodromic Deformations
• Gravitational instantons with faster than quadratic curvature decay (II)

Cited by in corpus (7)

• On toric Hermitian ALF gravitational instantons
• Smooth asymptotics for collapsing Calabi-Yau metrics
• On the geometry of asymptotically flat manifolds
• Collapsing geometry of hyperkähler 4-manifolds and applications
• Elliptic analysis on collapsing gravitational instantons modelled using the Gibbons-Hawking ansatz
• G${}_2$ manifolds with nodal singularities along circles
• Asymptotically Calabi metrics and weak Fano manifolds