Rigidity of four-dimensional compact manifolds with harmonic Weyl tensor

被引：0
作者：
Ernani Ribeiro
机构：
[1] Universidade Federal do Ceará - UFC,Departamento de Matemática, Campus do Pici
来源：
Annali di Matematica Pura ed Applicata (1923 -) | 2016年 / 195卷
关键词：
Einstein manifolds; Biorthogonal curvature; 4-Manifolds; Primary 53C21; 53C20; Secondary 53C25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove that a 4-dimensional compact manifold M4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M^4$$\end{document} with harmonic Weyl tensor must be either locally conformally flat or isometric to a complex projective space CP2,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {CP}^2,$$\end{document} provided that the biorthogonal (sectional) curvature satisfies a suitable pinching condition. In particular, we improve the pinching constants considered by some preceding works on a rigidity result for 4-dimensional compact manifolds.
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页码：2171 / 2181
页数：10
相关论文
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