Gravitational instantons of type $D_k$ and a generalization of the   Gibbons-Hawking Ansatz
  We describe a quaternionic-based Ansatz generalizing the Gibbons-Hawking Ansatz to a class of hyperk\"ahler metrics with hidden symmetries. We then apply it to obtain explicit expressions for gravitational instanton metrics of type $D_k$. 
Radu A. Ionas
math.DG hep-th math.AG