On Conformally Kaehler, Einstein Manifolds

Abstract

We prove that any compact complex surface with positive first Chern class admits an Einstein metric which is conformally related to a Kaehler metric. The key new ingredient is the existence of such a metric on the blow-up of the complex projective plane at two distinct points.

45 pages, 9 figures. Simplified proof of Lemma 25. Several minor corrections to section 5

References in corpus (4)

• Algebraic surfaces and Seiberg-Witten invariants
• Bach-flat asymptotically locally Euclidean metrics
• Unstable products of smooth curves
• Toric selfdual Einstein metrics on compact orbifolds

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• Future Directions of Research in Geometry: A Summary of the Panel Discussion at the 2007 Midwest Geometry Conference
• The mass of the product of spheres
• Special biconformal changes of Kähler surface metrics
• On Optimal 4-Dimensional Metrics