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 (1)

• Toric selfdual Einstein metrics on compact orbifolds

Cited by in corpus (2)

• Future Directions of Research in Geometry: A Summary of the Panel Discussion at the 2007 Midwest Geometry Conference
• On Optimal 4-Dimensional Metrics