Homogeneous almost quaternion-Hermitian manifolds

被引：0
作者：
Andrei Moroianu
Mihaela Pilca
Uwe Semmelmann
机构：
[1] Université de Versailles-St Quentin,Laboratoire de Mathématiques
[2] Universität Regensburg,Fakultät für Mathematik
[3] “Simion Stoilow” of the Romanian Academy,Institute of Mathematics
[4] Universität Stuttgart,Institut für Geometrie und Topologie, Fachbereich Mathematik
来源：
Mathematische Annalen | 2013年 / 357卷
关键词：
Primary 53C30; 53C35; 53C15; Secondary 17B22;
D O I：
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中图分类号：
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摘要：
An almost quaternion-Hermitian structure on a Riemannian manifold \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(M^{4n},g)$$\end{document} is a reduction of the structure group of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M$$\end{document} to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{Sp}(n)\mathrm{Sp}(1)\subset \text{ SO }(4n)$$\end{document}. In this paper we show that a compact simply connected homogeneous almost quaternion-Hermitian manifold of non-vanishing Euler characteristic is either a Wolf space, or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{S }^2\times \mathbb{S }^2$$\end{document}, or the complex quadric \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{ SO }(7)/\mathrm{U}(3)$$\end{document}.
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页码：1205 / 1216
页数：11
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