RIGIDITY OF GRADIENT RICCI SOLITONS

被引：178

作者：

Petersen, Peter ^{[1
]}

Wylie, William ^{[2
]}

机构：

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

[2] Univ Penn, Dept Math, David Rittenhouse Lab, Philadelphia, PA 19104 USA

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2009年 / 241卷 / 02期

关键词：

complete manifold; constant scalar curvature; Ricci soliton; Einstein manifold; GEOMETRY;

D O I：

10.2140/pjm.2009.241.329

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define a gradient Ricci soliton to be rigid if it is a flat bundle N x(Gamma) R(k) where N is Einstein. It is known that not all gradient solitons are rigid. Here we offer several natural conditions on the curvature that characterize rigid gradient solitons. Other related results on rigidity of Ricci solitons are also explained in the last section.

引用

页码：329 / 345

页数：17

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