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Anti-self-dual bihermitian structures on inoue surfaces

Akira Fujiki Osaka University Massimiliano Pontecorvo Universit´a Roma Tre

Differential Geometry mathscidoc:1609.10177

Journal of Differential Geometry, 85, (1), 15-71, 2010
In this article we show that any hyperbolic Inoue surface (also called Inoue-Hirzebruch surface of even type) admits anti-self-dual bihermitian structures. The same result holds for any of its small deformations as far as its anti-canonical system is non-empty. Similar results are obtained for parabolic Inoue surfaces. Our method also yields a family of anti-self-dual hermitian metrics on any half Inoue surface. We use the twistor method of Donaldson-Friedman [13] for the proof.
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@inproceedings{akira2010anti-self-dual,
  title={ANTI-SELF-DUAL BIHERMITIAN STRUCTURES ON INOUE SURFACES},
  author={Akira Fujiki, and Massimiliano Pontecorvo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911214617007907834},
  booktitle={Journal of Differential Geometry},
  volume={85},
  number={1},
  pages={15-71},
  year={2010},
}
Akira Fujiki, and Massimiliano Pontecorvo. ANTI-SELF-DUAL BIHERMITIAN STRUCTURES ON INOUE SURFACES. 2010. Vol. 85. In Journal of Differential Geometry. pp.15-71. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911214617007907834.
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