HYPERKÄHLER STRUCTURE OF THE TAUB-NUT METRIC

The Taub-NUT four-dimensional space-time can be obtained from Euclidean eight-dimensional one through a momentum map construction; the HKLR theorem 9] guarantees the hyperkähler structure of R ⁸ descends to a hyperkähler structure in the Taub-NUT space. Here we present a detailed and fully explicit construction of the hyperkähler structure of a space-time with a Taub-NUT metric.