ON LOCALLY CONFORMALLY FLAT GRADIENT SHRINKING RICCI SOLITONS

被引：46

作者：

Cao, Xiaodong ^{[1
]}

Wang, Biao ^{[1
]}

Zhang, Zhou ^{[2
]}

机构：

[1] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2011年 / 13卷 / 02期

基金：

美国国家科学基金会;

关键词：

Gradient shrinking Ricci soliton; locally conformally flat;

D O I：

10.1142/S0219199711004191

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we first apply an integral identity on Ricci solitons to prove that closed locally conformally flat gradient Ricci solitons are of constant sectional curvature. We then generalize this integral identity to complete noncompact gradient shrinking Ricci solitons, under the conditions that the Ricci curvature is bounded from below and the Riemannian curvature tensor has at most exponential growth. As a consequence, we classify complete locally conformally flat gradient shrinking Ricci solitons with Ricci curvature bounded from below.

引用

页码：269 / 282

页数：14

共 26 条

[1]

Böhm C, 2008, ANN MATH, V167, P1079

[2]

Cao HD, 1996, ELLIPTIC AND PARABOLIC METHODS IN GEOMETRY, P1

[3] Compact gradient shrinking Ricci solitons with positive curvature operator [J].