Royal Society Publishing

Self-Duality in Four-Dimensional Riemannian Geometry

M. F. Atiyah, N. J. Hitchin, I. M. Singer


We present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis. In particular we apply this to the self-dual Yang-Mills equations in Euclidean 4-space and compute the number of moduli for any compact gauge group. Results previously announced are treated with full detail and extended in a number of directions.

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