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Conformally Kähler, Einstein–Maxwell metrics on Hirzebruch surfaces

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In this note, we prove that a special family of Killing potentials on certain Hirzebruch complex surfaces, found by Futaki and Ono [18], gives rise to new conformally Kähler, Einstein–Maxwell metrics. The correspondent Kähler metrics are ambitoric [7, 9] but they are not given by the Calabi ansatz [31]. This answers in positive questions raised in [18, 19].

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Acknowledgements

This paper is part of the author’s Ph.D. thesis. The author would like to thank his thesis supervisor Vestislav Apostolov for his invaluable advice and for sharing his insights with him. The author is also grateful to Eveline Legendre, who kindly shared with him her observations used in the proof of Theorem 6.4. He would also like to thank Abdellah Lahdili and Lars Martin Sektnan for enlightening discussions, the Federal University of Ouro Preto and Université du Québec à Montréal for their financial support, and the referee for his careful reading and suggestions that greatly improved the text.

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  1. Département de Mathématiques, Université du Québec à Montréal, Montréal, Canada

    Isaque Viza de Souza

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Correspondence to Isaque Viza de Souza.

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Viza de Souza, I. Conformally Kähler, Einstein–Maxwell metrics on Hirzebruch surfaces. Ann Glob Anal Geom 59, 263–284 (2021). https://doi.org/10.1007/s10455-020-09749-y

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