Einstein Metrics, Complex Surfaces, and Symplectic 4-Manifolds

Mathematics – Differential Geometry

Scientific paper

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12 pages, LaTeX2e. Final version, to appear in Math. Proc. Camb. Phil. Soc. (Preliminary version appeared in informal lecture-

Scientific paper

Which smooth compact 4-manifolds admit an Einstein metric with non-negative
Einstein constant? A complete answer is provided in the special case of
4-manifolds that also happen to admit either a complex structure or a
symplectic structure.

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