Kaehler flat manifolds

KAREL DEKIMPE; MAREK HALENDA; ANDRZEJ SZCZEPANSKI

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Kaehler flat manifolds

机译：Kaehler平面歧管

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摘要

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

机译：使用Johnson-Rees [9]的准则，我们列出了所有四维和六维平面Kaehler流形。我们计算它们的R-同调性，包括霍奇数。作为推论，我们将维度为3的所有平面复杂流形分类，其整体性组为SU（3）的子组。此外，我们定义了一系列平面Kaehler流形，它们是定向Hantzsche-Wendt Riemannian流形的泛化[14]。

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来源
《Journal of the Mathematical Society of Japan》 |2009年第2期|363-377|共15页
作者
KAREL DEKIMPE; MAREK HALENDA; ANDRZEJ SZCZEPANSKI;
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作者单位

K. U. Leuven Campus Kortrijk Univcrsitaire Campus B-8500 Kortrijk Belgium;

Institute of Mathematics University of Gdansk ul. Wita Stwosza 57 80-952 Gdansk Poland;

Institute of Mathematics University of Gdansk ul. Wita Stwosza 57 80-952 Gdansk Poland;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
bieberbach group; flat manifold; kaehler manifold; hantzsche-wendt manifold; hodge diamond; hyperelliptic variety;

机译：比伯巴赫集团扁平歧管凯勒流形;汉茨-温特流形;大杂烩钻石高椭圆变种;

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专利

1. On 4-dimensional locally conformally flat almost Kaehler manifolds [J] . W. Krolikowski Archivum Mathematicum . 2006,第3期

机译：在4维局部保形的几乎Kaehler流形上
2. Totally real bisectional curvature, Bochner-Kaehler and Einstein-Kaehler manifolds [J] . Bang-Yen Chen, Franki Dillen Differential geometry and its applications . 1999,第2期

机译：完全二等分的曲率，Bochner-Kaehler和Einstein-Kaehler流形
3. Totally real bisectional curvature, Bochner-Kaehler and Einstein-Kaehler manifolds [J] . Bang-Yen Chen, Franki Dillen Differential geometry and its applications . 1999,第2期

机译：完全二等分的曲率，Bochner-Kaehler和Einstein-Kaehler流形
4. Hodge decomposition theorem on strongly Kaehler Finsler manifolds [C] . ZHONG Chunping, ZHONG Tongde, Chinese Academy of Sciences, International Conference on the Theory of Functions of Several Complex Variables . 2006

机译：霍尔德·分解定理强劲的Kaehler Finsler歧管
5. A twistor-sphere of generalized Kaehler potentials on hyperkaehler manifolds [D] . Dyckmanns, Malte 2011

机译：超kaehler流形上广义Kaehler势的扭转球
6. Generic Submanifolds of Nearly Kaehler Manifolds with Certain Parallel Canonical Structure [O] . Qingqing Zhu, Biaogui Yang 2014

机译：具有一定平行规范结构的几乎Kaehler流形的通用子流形
7. Unipotent flat bundles and Higgs bundles over compact Kaehler manifolds [O] . Lekaus, Silke 2003

机译：紧凑型Kaehler歧管上的单能扁平束和希格斯束
8. A-Genus on Non-Spin Manifolds with S1 Actions and the Classification of Positive Quaternion-Kaehler 12-Manifolds. [R] . Herrera, H., Herrera, R. 2001

机译：具有s1作用的非自旋流形的a族和正四元数 - Kaehler 12-流形的分类。

Kaehler flat manifolds

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