On toric Hermitian ALF gravitational instantons (Q2696105)

The authors give a classification of toric, Hermitian, Ricci flat, ALF Riemannian metrics in 4 dimensions, including metrics with conic singularities. One conclude, that the only smooth examples examples are one hand the hyperKahler ALF metrics, and on another hand, the Kerr, Taub-NUT, and Chen-Teo metrics. The authors provide also explicit examples with conical singularities, with many distinct topologies. Explicit formula were given. In order to find the classification the authors formulate and prove 2 important theorems