Einstein Metrics, Complex Surfaces, and Symplectic 4-Manifolds

Abstract

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.

12 pages, LaTeX2e. Final version, to appear in Math. Proc. Camb. Phil. Soc. (Preliminary version appeared in informal lecture-note volume in honor of Fujiki's 60th birthday.)

References in corpus (1)

• On Conformally Kaehler, Einstein Manifolds

Cited by in corpus (4)

• Smooth Yamabe invariant and surgery
• Kodaira Dimension in Low Dimensional Topology
• On Einstein metrics, normalized Ricci flow and smooth structures on $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$
• Sharp version of the Goldberg-Sachs theorem