On Compact Manifolds with Harmonic Curvature and Positive Scalar Curvature

被引：8

作者：

Fu, Hai-Ping ^{[1
]}

机构：

[1] Nanchang Univ, Dept Math, Nanchang 330031, Jiangxi, Peoples R China

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2017年 / 27卷 / 04期

关键词：

Einstein manifold; Harmonic curvature; Rigidity;

D O I：

10.1007/s12220-017-9798-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M-n (n >= 3) be an n-dimensional compact Riemannian manifold with harmonic curvature and positive scalar curvature. Assume that M-n satisfies some integral pinching conditions. We give some rigidity theorems. In particular, Theorems 1.4 and 1.10 are sharp for our conditions have the additional properties of being sharp. By this, we mean that we can precisely characterize the case of equality.

引用

页码：3120 / 3139

页数：20

共 32 条

[1]

[Anonymous], ARXIV10120342

[2]

[Anonymous], 1952, Comment. Math. Helv, DOI [DOI 10.1007/BF02564308, 10.1007/BF02564308]

[3]

Aubin T., 1998, Springer Monographs in Mathematics

[4]

Besse A. L., 2007, EINSTEIN MANIFOLDS

[5]

BOURGUIGNON JP, 1982, LECT NOTES MATH, V949, P35

[6]

Branson T, 2000, MATH RES LETT, V7, P245

[7] Moduli spaces of critical Riemannian metrics with Ln/2 norm curvature bounds [J].

Chen, Xiuxiong ;

Weber, Brian .

ADVANCES IN MATHEMATICS, 2011, 226 (02) :1307-1330

[8] Complete noncompact manifolds with harmonic curvature [J].

Chu, Yawei .

FRONTIERS OF MATHEMATICS IN CHINA, 2012, 7 (01) :19-27

[9] ON COMPACT RIEMANNIAN-MANIFOLDS WITH HARMONIC CURVATURE [J].

DERDZINSKI, A .

MATHEMATISCHE ANNALEN, 1982, 259 (02) :145-152

[10]

DeTurck D. M., 1989, Forum Math., V1, P377, DOI DOI 10.1515/FORM.1989.1.377

← 1 2 3 4 →