Resumen de Bihermitian metrics on Hopf surfaces

Vestislav Apostolov, Georges Dloussky

• Inspired by a construction due to Hitchin~\cite{hitchin4}, we produce strongly bihermitian metrics on certain Hopf complex surfaces, which integrate the locally conformally K\"ahler 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.