Abstract
The notion of Kodaira dimension has recently been extended to general almost complex manifolds. In this paper we focus on the Kodaira dimension of almost Kähler manifolds, providing an explicit computation for a family of almost Kähler threefolds on the differentiable manifold underlying a Nakamura manifold. We concentrate also on the link between Kodaira dimension and the curvature of the canonical connection of an almost Kähler manifold and show that in the previous example (and in another one obtained from a Kodaira surface) the Ricci curvature of the almost Kähler metric vanishes for all the members of the family.
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Acknowledgements
The authors express their gratitude to Weiyi Zhang for having introduced them to the subject of Kodaira dimension for almost complex manifolds. We also thank Tian-Jun Li for having brought to our attention the reference [5] and Valentino Tosatti for his comments on a previous version of this paper.
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This work was partially supported by the Project PRIN 'Varietà reali e complesse: geometria, topologia e analisi armonica' and by GNSAGA of INdAM. Andrea Cattaneo is also supported by the ‘Grant de Bartolomeis’, a fellowship in memory of Prof. Paolo de Bartolomeis.
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Cattaneo, A., Nannicini, A. & Tomassini, A. Kodaira dimension of almost Kähler manifolds and curvature of the canonical connection. Annali di Matematica 199, 1815–1842 (2020). https://doi.org/10.1007/s10231-020-00944-z
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DOI: https://doi.org/10.1007/s10231-020-00944-z