Bach-flat gradient steady Ricci solitons

被引：57

作者：

Cao, Huai-Dong ^{[1
]}

Catino, Giovanni ^{[2
]}

Chen, Qiang ^{[1
]}

Mantegazza, Carlo ^{[3
]}

Mazzieri, Lorenzo ^{[3
]}

机构：

[1] Lehigh Univ, Dept Math, Bethlehem, PA 18015 USA

[2] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

[3] Scuola Normale Super Pisa, I-56126 Pisa, Italy

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 49卷 / 1-2期

关键词：

FLOW; UNIQUENESS;

D O I：

10.1007/s00526-012-0575-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove that any n-dimensional (n a parts per thousand yen 4) complete Bach-flat gradient steady Ricci soliton with positive Ricci curvature is isometric to the Bryant soliton. We also show that a three-dimensional gradient steady Ricci soliton with divergence-free Bach tensor is either flat or isometric to the Bryant soliton. In particular, these results improve the corresponding classification theorems for complete locally conformally flat gradient steady Ricci solitons in Cao and Chen (Trans Am Math Soc 364:2377-2391, 2012) and Catino and Mantegazza (Ann Inst Fourier 61(4):1407-1435, 2011).

引用

页码：125 / 138

页数：14

共 16 条

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