Kähler flat manifolds

Karel DEKIMPE; Marek HAŁENDA; Andrzej SZCZEPAŃSKI

doi:10.2969/jmsj/06120363

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Kähler flat manifolds

Karel DEKIMPE, Marek HAŁENDA ^†, Andrzej SZCZEPAŃSKI ^†

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Keywords: Bieberbach group, flat manifold, Kähler manifold, Hantzsche-Wendt manifold, Hodge diamond, hyperelliptic variety

JOURNAL FREE ACCESS

2009 Volume 61 Issue 2 Pages 363-377

DOI https://doi.org/10.2969/jmsj/06120363

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Abstract

Using a criterion of Johnson-Rees [9] we give a list of all four and six dimensional flat Kähler manifolds. We calculate their R–cohomology, including the Hodge numbers. As a corollary, we classify all flat complex manifolds of dimension 3 whose holonomy groups are subgroups of SU(3). Moreover, we define a family of flat Kähler manifolds which are generalizations of the oriented Hantzsche-Wendt Riemannian manifolds [14].

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