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?
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?
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).