Dₖ gravitational instantons and Nahm equations

We construct Dk Asymptotically Locally Flat gravitational instantons as moduli spaces of solutions of Nahm equations.This allows us to find their twistor spaces and Kahler potentials. IntroductionGravitational instantons are four-dimensional manifolds with a self-dual curvature tensor.They can be compact (K3 and T 4 ) or noncompact.Asymptotically Locally Euclidean (ALE) instantons are gravitational instantons that approach R 4 /r at infinity, where F is a finite subgroup of SU(2).These were constructed by Gibbons and Hawking [1] for F = Zj.and by Kronheimer [2] for all possible F.