On Conformally Kaehler, Einstein Manifolds

Mathematics – Differential Geometry

Scientific paper

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

Scientific paper

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.

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