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arXiv · 0803.3734

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

Claude LeBrun
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Abstract

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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Claude LeBrun. 2008-05-09. The Einstein-Maxwell Equations, Extremal Kahler Metrics, and Seiberg-Witten Theory. https://arxiv.org/abs/0803.3734

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