Self-duality in four-dimensional Riemannian geometry

19781,457 citationsJournal Article

Authors

Michael Atiyah · Mathematical Institute of the Slovak Academy of Sciences

Nigel Hitchin · Mathematical Institute of the Slovak Academy of Sciences

I. M. Singer · University of California, Berkeley

Abstract

Abstract 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.

Topics & Keywords

Advanced Algebra and Geometry Black Holes and Theoretical Physics advanced mathematical theories

Publication Details

Published in: Proceedings of the Royal Society of London A Mathematical and Physical Sciences

Volume 362, Issue 1711, pp. 425-461

DOI: 10.1098/rspa.1978.0143

Field-Weighted Citation Impact: 28.43

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Self-duality in four-dimensional Riemannian geometry

Authors

Abstract

Topics & Keywords

Publication Details