Journal of the Mathematical Society of Japan

Kähler flat manifolds

Karel DEKIMPE, Marek HAŁENDA, and Andrzej SZCZEPAŃSKI

Full-text: Open access

Abstract

Using a criterion of Johnson-Rees [9] we give a list of all four and six dimensional flat Kähler manifolds. We calculate their $\mbi{R}$–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].

Article information

Source
J. Math. Soc. Japan Volume 61, Number 2 (2009), 363-377.

Dates
First available in Project Euclid: 13 May 2009

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1242220714

Digital Object Identifier
doi:10.2969/jmsj/06120363

Mathematical Reviews number (MathSciNet)
MR2532893

Subjects
Primary: 57N16: Geometric structures on manifolds [See also 57M50]
Secondary: 20H15: Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25] 14J32: Calabi-Yau manifolds

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

Citation

DEKIMPE, Karel; HAŁENDA, Marek; SZCZEPAŃSKI, Andrzej. Kähler flat manifolds. J. Math. Soc. Japan 61 (2009), no. 2, 363--377. doi:10.2969/jmsj/06120363. http://projecteuclid.org/euclid.jmsj/1242220714.


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