From ALE to ALF gravitational instantons

Auvray, Hugues

doi:10.1112/S0010437X18007030

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From ALE to ALF gravitational instantons

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Auvray, Hugues
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1112/S0010437X18007030
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arXiv:1304.3342.pdf
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Citation

Auvray, H. (2018). From ALE to ALF gravitational instantons. Compositio Mathematica, 154(6), 1159-1221. doi:10.1112/S0010437X18007030.

Cite as: https://hdl.handle.net/21.11116/0000-0004-46BC-A

Abstract

In this article, we give an analytic construction of ALF hyperk\"ahler metrics on smooth deformations of the Kleinian singularity $}mathbb{C}^2/D_k$ , with $D_k$ the binary dihedral group of order $4k, k \geq 2$. More precisely, we start from the ALE hyperk\"ahler metrics constructed on these spaces by Kronheimer, and use analytic methods, e.g. resolution of a Monge-Amp\`{e}re equation, to produce ALF hyperk\"ahler metrics with the same associated K\"ahler classes.