Open Access
February 2012 On Einstein, Hermitian 4-manifolds
Claude LeBrun
J. Differential Geom. 90(2): 277-302 (February 2012). DOI: 10.4310/jdg/1335230848


Let $(M, h)$ be a compact 4-dimensional Einstein manifold, and suppose that $h$ is Hermitian with respect to some complex structure $J$ on $M$. Then either $(M, J, h)$ is Kähler-Einstein, or else, up to rescaling and isometry, it is one of the following two exceptions: the Page metric on $\mathbb{CP}_2\#\overline{\mathbb{CP}}_2$, or the Einstein metric on $\mathbb{CP}_2\#2\overline{\mathbb{CP}}_2$ discovered in "On conformally Kähler, Einstein manifolds," J. Amer. Math. Soc. 21 (2008), pp. 1137–1168.


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Claude LeBrun. "On Einstein, Hermitian 4-manifolds." J. Differential Geom. 90 (2) 277 - 302, February 2012.


Published: February 2012
First available in Project Euclid: 24 April 2012

zbMATH: 1254.53076
MathSciNet: MR2899877
Digital Object Identifier: 10.4310/jdg/1335230848

Rights: Copyright © 2012 Lehigh University

Vol.90 • No. 2 • February 2012
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