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ISSN 1088-6834(e) ISSN 0894-0347(p)

On conformally Kähler, Einstein manifolds

Author(s): Xiuxiong Chen; Claude LeBrun; Brian Weber
Journal: J. Amer. Math. Soc. 21 (2008), 1137-1168.
MSC (2000): Primary 53C55; Secondary 14J80, 53A30, 53C25
Posted: January 28, 2008
MathSciNet review: 2425183
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Abstract: We prove that any compact complex surface with admits an Einstein metric which is conformally related to a Kähler metric. The key new ingredient is the existence of such a metric on the blow-up $\mathbb{CP}_2\char93 2\overline{\mathbb{CP}_2}$ of the complex projective plane at two distinct points.

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