Bihermitian metrics on Hopf surfaces

Inspired by a construction due to Hitchin~\cite{hitchin4}, we produce strongly bihermitian metrics on certain Hopf complex surfaces, which integrate the locally conformally Kähler metrics found by Gauduchon–Ornea~\cite{GO}. We also show that the Inoue complex surfaces with $b_2=0$ do not admit bihermitian metrics. This completes the classification of the compact complex surfaces admitting strongly bihermitian metrics.

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Published 1 January 2008