Conformally flat 3-manifolds with constant scalar curvature

被引：9

作者：

Cheng, QM ^{[1
]}

Ishikawa, S

Shiohama, K

机构：

[1] Josai Univ, Fac Sci, Dept Math, Sakado, Saitama 3500290, Japan

[2] Saga Univ, Dept Math, Saga 8408502, Japan

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 1999年 / 51卷 / 01期

关键词：

space form; conformally flat manifold; constant scalar curvature and Ricci curvature tensor;

D O I：

10.2969/jmsj/05110209

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify complete conformally flat three dimensional Riemannian manifolds with constant scalar curvature and constant squared norm of Ricci curvature tensor by applying the Generalized Maximum Principle due to H. Omori.

引用

页码：209 / 226

页数：18

共 50 条

[31] The scalar curvature deformation equation on locally conformally flat manifolds of higher dimensions
Yan, Yu
[J]. PACIFIC JOURNAL OF MATHEMATICS, 2008, 237 (02) : 373 - 398
[32] Geodesic and conformally Reeb vector fields on flat 3-manifolds
Becker, Tilman
[J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2023, 89
[33] CONFORMALLY FLAT 3-MANIFOLDS WITH COMPACT AUTOMORPHISM-GROUPS
KAMISHIMA, Y
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1988, 38 : 367 - 378
[34] Two classes of conformally flat contact metric 3-manifolds
Gouli-Andreou F.
Xenos P.J.
[J]. Journal of Geometry, 1999, 64 (1-2) : 80 - 88
[35] Contractible 3-manifolds and positive scalar curvature (II)
Wang, Jian
[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2024, 26 (02) : 537 - 572
[36] Compactness for conformal metrics with constant Q curvature on locally conformally flat manifolds
Qing, J
Raske, D
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2006, 26 (03) : 343 - 356
[37] Compactness for conformal metrics with constant Q curvature on locally conformally flat manifolds
Jie Qing
David Raske
[J]. Calculus of Variations and Partial Differential Equations, 2006, 26 : 343 - 356
[38] Convex-cocompactness of Kleinian groups and conformally flat manifolds with positive scalar curvature
Izeki, H
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (12) : 3731 - 3740
[39] CONFORMALLY FLAT STRUCTURES ON 3-MANIFOLDS - EXISTENCE PROBLEM .1.
KAPOVICH, ME
[J]. SIBERIAN MATHEMATICAL JOURNAL, 1989, 30 (05) : 712 - 722
[40] Conformally flat manifolds with nonnegative Ricci curvature
Carron, G
Herzlich, M
[J]. COMPOSITIO MATHEMATICA, 2006, 142 (03) : 798 - 810

← 1 2 3 4 5 →