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

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

1995-06-05

arxiv.org/abs/dg-ga/9506002v1

Mathematics

Differential Geometry

10 pages, latex

Scientific paper

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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