Anti-self-dual bihermitian structures on Inoue surfaces

Details Anti-self-dual bihermitian structures on Inoue surfaces Anti-self-dual bihermitian structures on Inoue surfaces

2009-03-09

arxiv.org/abs/0903.1320v1

Mathematics

Differential Geometry

69 pages,

Scientific paper

We show that any hyperbolic Inoue surface (or Inoue-Hirzebruch surface of even type) admits anti-self-dual bihermitian structures. The same result also 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 anti-self-dual hermitian metrics on any half Inoue surface. We use the twistor method of Donaldson-Friedman for the proof.

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