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Free keywords:
Mathematics, Differential Geometry
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.
