Invariant metrics of positive Ricci curvature on principal bundles

被引：0
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作者：
Peter B. Gilkey
JeongHyeong Park
Wilderich Tuschmann
机构：
[1] Mathematics Department,
[2] University of Oregon,undefined
[3] Eugene,undefined
[4] OR 97403,undefined
[5] USA (e-mail: gilkey@math.uoregon.edu) ,undefined
[6] Department of Mathematics,undefined
[7] Honam University,undefined
[8] Seobongdong 59,undefined
[9] Kwangsanku,undefined
[10] Kwangju,undefined
[11] 506-090,undefined
[12] South Korea,undefined
[13] (e-mail: jhpark@honam.honam.ac.kr) ,undefined
[14] Max-Planck-Institut für Mathematik,undefined
[15] Gottfried-Claren-Strasse 26,undefined
[16] D-53225 Bonn,undefined
[17] Germany (e-mail: tusch@mis.mpg.de) ,undefined
来源：
Mathematische Zeitschrift | 1998年 / 227卷
关键词：
Mathematics Subject Classification: Mathematics Subject Classification (1991): 53C20.;
D O I：
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学科分类号：
摘要：
Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $Y$\end{document} be a compact connected Riemannian manifold with a metric of positive Ricci curvature. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\pi:P\rightarrow Y$\end{document} be a principal bundle over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $Y$\end{document} with compact connected structure group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $G$\end{document}. If the fundamental group of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $P$\end{document} is finite, we show that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $P$\end{document} admits a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $G$\end{document} invariant metric with positive Ricci curvature so that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\pi$\end{document} is a Riemannian submersion.
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页码：455 / 463
页数：8
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