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arXiv · 1404.7662

Manifolds which are complex and symplectic but not Kähler

Giovanni Bazzoni·Vicente Muñoz
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Abstract

The first example of a compact manifold admitting both complex and symplectic structures but not admitting a Kähler structure is the renowned Kodaira-Thurston manifold. We review its construction and show that this paradigm is very general and is not related to the fundamental group. More specifically, we prove that the simply-connected $8$-dimensional compact manifold of [\textsc{M. Fernández and V. Muñoz}, \emph{An 8-dimensional non-formal simply connected symplectic manifold}, Ann. of Math. (2) \textbf{167}, no. 3, 1045--1054, 2008.] admits both symplectic and complex structures but does not carry Kähler metrics.

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Giovanni Bazzoni, Vicente Muñoz. 2014-04-30. Manifolds which are complex and symplectic but not Kähler. https://arxiv.org/abs/1404.7662

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