On conformally Kähler, Einstein manifolds

Chen, Xiuxiong¹ ; LeBrun, Claude² ; Weber, Brian²

¹ Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Dr, Madison, Wisconsin 53706-1388
² Department of Mathematics, State University of New York, Stony Brook, New York 11794-3651

Journal of the American Mathematical Society, Tome 21 (2008) no. 4, pp. 1137-1168

Résumé

We prove that any compact complex surface with $c_1>0$ 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 $\mathbb {CP}_2\# 2\overline {\mathbb {CP}_2}$ of the complex projective plane at two distinct points.

Détail

DOI : 10.1090/S0894-0347-08-00594-8

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