On the classification of gradient Ricci solitons

被引：139

作者：

Petersen, Peter ^{[1
]}

Wylie, William

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

GEOMETRY & TOPOLOGY | 2010年 / 14卷 / 04期

关键词：

CURVATURE; MANIFOLDS; RIGIDITY;

D O I：

10.2140/gt.2010.14.2277

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the only shrinking gradient solitons with vanishing Weyl tensor and Ricci tensor satisfying a weak integral condition are quotients of the standard ones S-n, Sn-1 x R and R-n. This gives a new proof of the Hamilton-Ivey-Perelman classification of 3-dimensional shrinking gradient solitons. We also show that gradient solitons with constant scalar curvature and suitably decaying Weyl tensor when noncompact are quotients of H-n, Hn-1 x R, R-n, Sn-1 x R or S-n

引用

页码：2277 / 2300

页数：24

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