Toda Fields of SO(3) Hyper-Kahler Metrics

We examine the Toda frame formulation of the SO(3)-invariant hyper-Kahler 4-metrics, namely Eguchi-Hanson, Taub-NUT and Atiyah-Hitchin. Our method exploits the presence of a rotational SO(2) isometry, leading to the explicit construction of all three complex structures as a singlet plus a doublet. The Atiyah-Hitchin metric on the moduli space of BPS SU(2) monopoles with magnetic charge 2 is purely rotational.