Abstract
We show in a simple and systematical way the self-duality constraints of certain SU(2) gauge fields can be used to rediscover the Einstein metrics. Starting with a metric tensor with two unknown functions, the self-duality constraints of the SU(2) gauge field obtained from the spin connections are studied. The general Taub-NUT-De Sitter metric is found to emerge quite simply as a solution, though the riemannian tensor of the metric itself is not self-dual in the general case. Different interesting limiting cases, such as the Eguchi-Hanson metric, are also obtained directly from the constraint equations.
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