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The Einstein-Maxwell Equations, Extremal Kahler Metrics, and Seiberg-Witten Theory

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arxiv 0803.3734 v2 pith:4HINDPUY submitted 2008-03-26 math.DG gr-qcmath.AG

Claude LeBrun This is my paper · ORCID
classification math.DGgr-qcmath.AG
keywords extremalkahlermetricsseiberg-witteneinstein-maxwellequationsproblemthen
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The Einstein-Maxwell equations on a smooth compact 4-manifold are reformulated as a purely Riemannian variational problem analogous to Calabi's variational problem for extremal Kahler metrics. Next, Seiberg-Witten theory is used to show that these two problems are in fact intimately related. Extremal Kahler metrics are then used to probe the limits of Seiberg-Witten curvature estimates. The article then concludes with a brief survey of some recent results on extremal Kahler metrics.

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    New infinite families of supersymmetric spindle-bolt solutions with branched lens-space boundaries are constructed, with on-shell actions matching equivariant localization.

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