Kahler flat manifolds

被引：18

作者：

Dekimpe, Karel ^{[1
]}

Halenda, Marek ^{[2
]}

Szczepanski, Andrzej ^{[2
]}

机构：

[1] Katholieke Univ Leuven, B-8500 Kortrijk, Belgium

[2] Univ Gdansk, Inst Math, PL-80952 Gdansk, Poland

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2009年 / 61卷 / 02期

关键词：

Bieberbach group; flat manifold; Kahler manifold; Hantzsche-Wendt manifold; Hodge diamond; hyperelliptic variety; BIEBERBACH-GROUPS;

D O I：

10.2969/jmsj/06120363

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using a criterion of Johnson-Rees [9] we give a list of all four and six dimensional flat Kahler 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 Kahler manifolds which are generalizations of tire oriented Hantzsche-Wendt Riemannian manifolds [14].

引用

页码：363 / 377

页数：15

共 17 条

[1] The motion groups of the Euclidean space (First essay)
Bieberbach, L
[J]. MATHEMATISCHE ANNALEN, 1911, 70 : 297 - 336
[2] Brown H., 1978, CRYSTALLOGRAPHIC GRO
[3] Computation of five- and six-dimensional Bieberbach groups
Cid, C
Schulz, T
[J]. EXPERIMENTAL MATHEMATICS, 2001, 10 (01) : 109 - 115
[4] Curtis C., 1987, Methods of representation theory, VII
[5] Spin structures on flat manifolds
Dekimpe, K.
Sadowski, M.
Szczepanski, A.
[J]. MONATSHEFTE FUR MATHEMATIK, 2006, 148 (04): : 283 - 296
[6] Three dimensional Euclidean spatial forms.
Hantzsche, W
Wendt, H
[J]. MATHEMATISCHE ANNALEN, 1935, 110 : 593 - 611
[7] HOLONOMY OF FLAT MANIFOLDS WITH B1=0
HILLER, H
SAH, CH
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 1986, 37 (146) : 177 - 187
[8] Johnson F. E. A., 1989, LONDON MATH SOC LECT, V150, P73
[9] KAHLER GROUPS AND RIGIDITY PHENOMENA
JOHNSON, FEA
REES, EG
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1991, 109 : 31 - 44
[10] Joyce D. D, 2000, COMPACT MANIFOLDS SP

← 1 2 →