Abstract
We classify compact self-dual almost-Kähler four-manifolds of positive type and zero type. In particular, using LeBrun’s result, we show that any self-dual almost-Kähler metric on a manifold which is diffeomorphic to \({{\mathbb {C}}}{{\mathbb {P}}}_{2}\) is the Fubini-Study metric on \({{\mathbb {C}}}{{\mathbb {P}}}_{2}\) up to rescaling. In case of negative type, we classify compact self-dual almost-Kähler four-manifolds with J-invariant ricci tensor.
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The author would like to thank Prof. Claude LeBrun for helpful comments. The author would like to thank the referee for helpful comments.
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Kim, I. Self-dual almost-Kähler four-manifolds. Ann Glob Anal Geom 65, 28 (2024). https://doi.org/10.1007/s10455-024-09958-9
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DOI: https://doi.org/10.1007/s10455-024-09958-9