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The Many Facets of GeometryA Tribute to Nigel Hitchin$
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Oscar Garcia-Prada, Jean Pierre Bourguignon, and Simon Salamon

Print publication date: 2010

Print ISBN-13: 9780199534920

Published to Oxford Scholarship Online: September 2010

DOI: 10.1093/acprof:oso/9780199534920.001.0001

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The Einstein‐Maxwell Equations, Extremal Kähler Metrics, and Seiberg‐Witten Theory

The Einstein‐Maxwell Equations, Extremal Kähler Metrics, and Seiberg‐Witten Theory

Chapter:
(p.17) III The Einstein‐Maxwell Equations, Extremal Kähler Metrics, and Seiberg‐Witten Theory
Source:
The Many Facets of Geometry
Author(s):

Claude LeBrun

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199534920.003.0003

Nigel Hitchin has played a key role in the exploration of four-dimensional Riemannian geometry, and in particular has made foundational contributions to the theory of self-dual manifolds, four-dimensional Einstein manifolds, spinc structures, and Kähler geometry. In the process, he called attention to the profound mathematical interest of beautiful geometric problems that had previously only been considered by physicists. This chapter focuses on an interesting relationship between the four-dimensional Einstein–Maxwell equations and Kähler geometry, and points out some fascinating open problems that directly impinge on this relationship.

Keywords:   Nigel Hitchin, Einstein–Maxwell equations, Kähler geometry, Riemannian geometry

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