A Kummer construction for gravitational instantons

Abstract

We give a simple and uniform construction of essentially all known deformation classes of gravitational instantons with ALF, ALG or ALH asymptotics and nonzero injectivity radius. We also construct new ALH Ricci flat metrics asymptotic to the product of a real line with a flat 3-manifold.

The construction of locally hyperkahler ALH spaces is corrected and completed

References in corpus (4)

• Gravitational Instantons of Type D_k
• Hyperkahler Metrics from Periodic Monopoles
• Singular Monopoles and Gravitational Instantons
• A mass for ALF manifolds

Cited by in corpus (8)

• Gravitational instantons with faster than quadratic curvature decay (III)
• Deformations of Nodal Kähler-Einstein Del Pezzo Surfaces with Discrete Automorphism Groups
• Complete non-compact Spin(7) manifolds from self-dual Einstein 4-orbifolds
• Harmonic forms on ALF gravitational instantons
• Degenerating Kähler-Einstein cones, locally symmetric cusps, and the Tian-Yau metric
• On the geometry of asymptotically flat manifolds
• Gravitational instantons of type $D_k$ and a generalization of the Gibbons-Hawking Ansatz
• Blowing up Chern-Ricci flat balanced metrics