Bihermitian metrics on Hopf surfaces

Details Bihermitian metrics on Hopf surfaces Bihermitian metrics on Hopf surfaces

2007-10-11

arxiv.org/abs/0710.2266v1

Mathematics

Differential Geometry

Scientific paper

Inspired by a construction due to Hitchin, we produce strongly bihermitian metrics on certain Hopf complex surfaces, which integrate the locally conformally Kaehler metrics found by Gauduchon and Ornea. We also show that the Inoue complex surfaces with zero second Betti number do not admit bihermitian metrics. This completes the classification of the compact complex surfaces admitting strongly bihermitian metrics.

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