Kodaira dimension of almost K\"ahler manifolds and curvature of the canonical connection

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 K\"ahler manifolds, providing an explicit computation for a family of almost K\"ahler threefolds on the differentiable manifold underlyi...

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Bibliographic Details
Main Authors Cattaneo, Andrea, Nannicini, Antonella, Tomassini, Adriano
Format Journal Article
LanguageEnglish
Published 29.08.2019
Subjects
Mathematics - Differential Geometry
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Summary: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 K\"ahler manifolds, providing an explicit computation for a family of almost K\"ahler 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 K\"ahler manifold, and show that in the previous example (and in another one obtained from a Kodaira surface) the Ricci curvature of the almost K\"ahler metric vanishes for all the members of the family.
DOI:10.48550/arxiv.1908.11328