Bihermitian metrics on Hopf surfaces

• Autores: Vestislav Apostolov, Georges Dloussky
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 5-6, 2008, págs. 827-840
• Idioma: inglés
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• Resumen

  • 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.