The Gibbons–Bando-Kasue-Nakajima conjecture on simply-connected Ricci-flat ALE instantons

A simply-connected Ricci-flat ALE instanton is a complete Riemannian manifold with vanishing Ricci curvature and asymptotically locally Euclidean geometry. Gibbons–Bando-Kasue-Nakajima conjecture. Any simply-connected Ricci-flat ALE instanton is hyper-Kähler. This formulation appears in the introduction as a simpler conjecture emerging from the rigidity question for the generalized positive mass theorem; the supplied text does not state whether this formulation is resolved.