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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.