Manifolds Which Are Complex and Symplectic But Not Kähler

Giovanni Bazzoni () and Vicente Muñoz ()
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Giovanni Bazzoni: Fakultät für Mathematik, Universität Bielefeld
Vicente Muñoz: Facultad de Matemáticas, Universidad Complutense de Madrid

A chapter in Essays in Mathematics and its Applications, 2016, pp 49-69 from Springer

Abstract: 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 eight-dimensional compact manifold of Fernández and Muñoz (Ann Math (2), 167(3):1045–1054, 2008) admits both symplectic and complex structures but does not carry Kähler metrics.

Keywords: Minimal Model; Complex Manifold; Symplectic Manifold; Symplectic Structure; Massey Product (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-31338-2_3

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DOI: 10.1007/978-3-319-31338-2_3

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