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Concerning my previous question Non simply connected HyperKähler 4-manifolds without ALE metrics the following question occurred to me:

Is there any open Ricci-flat ALE 4-manifold other than Hyper-Kahler ALE 4-manifolds?

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See Ioana Suvaina, ALE Ricci-flat metrics and deformations of quotient surface singularities, Remark 4.5 (this reference was also in one of the answers to your previous question).

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dissrtation of Hugues Auvray, tel.archives-ouvertes.fr/tel-00750891/document – Hassan Jolany Dec 29 '15 at 17:15

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