On Positive Sasakian Geometry

被引:0
|
作者
Charles P. Boyer
Krzysztof Galicki
Michael Nakamaye
机构
[1] University of New Mexico,Department of Mathematics and Statistics
来源
Geometriae Dedicata | 2003年 / 101卷
关键词
Fano varieties; positive Ricci curvature; Sasakian geometry;
D O I
暂无
中图分类号
学科分类号
摘要
A Sasakian structure \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{S}$$ \end{document}=(\xi,\eta,\Phi,g) on a manifold Mis called positiveif its basic first Chern class c1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{F}$$ \end{document}ξ) can be represented by a positive (1,1)-form with respect to its transverse holomorphic CR-structure. We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has positive Ricci curvature. This provides us with a new technique for proving the existence of positive Ricci curvature metrics on certain odd dimensional manifolds. As an example we give a completely independent proof of a result of Sha and Yang that for every nonnegative integer kthe 5-manifolds k#(S2×S3) admits metrics of positive Ricci curvature.
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页码:93 / 102
页数:9
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