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Polarized 4-Manifolds, Extremal Kähler Metrics, and S-W Theory

Claude LeBrun
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Abstract

Using Seiberg-Witten theory, it is shown that any Kaehler metric of constant negative scalar curvature on a compact 4-manifold M minimizes the L^2-norm of scalar curvature among Riemannian metrics compatible with a fixed decomposition H^2(M)=(H^+) + (H^-). This implies, for example, that any such metric on a minimal ruled surface must be locally symmetric.

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BibTeXRIS

Claude LeBrun. 1995-06-05. Polarized 4-Manifolds, Extremal Kähler Metrics, and S-W Theory. https://arxiv.org/abs/dg-ga/9506002

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