From ALE to ALF gravitational instantons. II

TL;DR

This paper extends the construction of ALF hyperkahler metrics from Kleinian singularities to their smooth deformations, using asymptotic analysis of ALE gravitational instantons.

Contribution

It generalizes previous work by constructing ALF hyperkahler metrics on deformed Kleinian singularities through asymptotic computations.

Findings

Successfully constructed ALF metrics on deformed singularities

Computed asymptotics of ALE gravitational instantons

Extended the class of known hyperkahler metrics

Abstract

This paper is the sequel of our previous article "From ALE to ALF gravitational instantons", where we constructed ALF hyperkahler metrics on minimal resolutions of dihedral Kleinian singularities. In the present article we generalize the construction to smooth deformations of these Kleinian singularities, with help of the computation of the asymptotics of the ALE gravitational instantons.