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On einstein, hermitian 4-manifolds

Claude LeBrun SUNY

Differential Geometry mathscidoc:1609.10253

Journal of Differential Geometry, 90, (2), 277-302, 2012
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 K¨ahler-Einstein, or else, up to rescaling and isometry, it is one of the following two exceptions: the Page metric on CP2#CP2, or the Einstein metric on CP2#2CP2 discovered in [8].
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@inproceedings{claude2012on,
  title={ON EINSTEIN, HERMITIAN 4-MANIFOLDS },
  author={Claude LeBrun},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913223643395605915},
  booktitle={Journal of Differential Geometry},
  volume={90},
  number={2},
  pages={277-302},
  year={2012},
}
Claude LeBrun. ON EINSTEIN, HERMITIAN 4-MANIFOLDS . 2012. Vol. 90. In Journal of Differential Geometry. pp.277-302. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913223643395605915.
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