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

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.

10 pages, latex

Cited by in corpus (1)

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