Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Manifolds which are complex and symplectic but not K\"ahler   The first example of a compact manifold admitting both complex and symplectic
structures but not admitting a K\"ahler 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. Fern\'{a}ndez and V. Mu\~{n}oz}, \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 K\"ahler metrics.

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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph