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

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dc.creatorLeBrun, Claude
dc.date2008-03-26
dc.date2008-05-09
dc.date.accessioned2026-07-07T09:37:41Z
dc.date.available2026-07-07T09:37:41Z
dc.descriptionThe 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.
dc.description21 pages, LaTeX2e. To appear in "The Many Facets of Geometry: a Tribute to Nigel Hitchin." Final version includes two new results, as well as many added references
dc.identifierhttps://arxiv.org/abs/0803.3734
dc.identifierhttp://arxiv.org/abs/0803.3734
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160547
dc.subjectDifferential Geometry
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectAlgebraic Geometry
dc.subject53C25; 57R57; 83C22
dc.titleThe Einstein-Maxwell Equations, Extremal Kahler Metrics, and Seiberg-Witten Theory
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