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Self-duality in four-dimensional Riemannian geometry
Proceedings of the Royal Society of London A Mathematical and Physical Sciences · 1978 · Vol. 362(1711) · pp. 425–461
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.
Advanced Algebra and GeometryBlack Holes and Theoretical Physicsadvanced mathematical theoriesDuality (order theory)Riemannian geometryMathematicsGeometryModuli spaceEuclidean geometryEuclidean spaceGauge (firearms)Space (punctuation)Pure mathematics
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