Rigidity of gradient Ricci solitons

Peter Petersen; William Wylie

doi:10.2140/pjm.2009.241.329

Rigidity of gradient Ricci solitons

Peter Petersen, William Wylie

Research output: Contribution to journal › Article › peer-review

173 Scopus citations

Abstract

We define a gradient Ricci soliton to be rigid if it is a flat bundle N ×_Γ R{double-struck}^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.

Original language	English (US)
Pages (from-to)	329-345
Number of pages	17
Journal	Pacific Journal of Mathematics
Volume	241
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2009.241.329
State	Published - Jun 2009
Externally published	Yes

Keywords

Complete manifold
Constant scalar curvature
Einstein manifold
Ricci soliton

ASJC Scopus subject areas

General Mathematics

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10.2140/pjm.2009.241.329

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abstract = "We define a gradient Ricci soliton to be rigid if it is a flat bundle N ×Γ R{double-struck}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.",

keywords = "Complete manifold, Constant scalar curvature, Einstein manifold, Ricci soliton",

author = "Peter Petersen and William Wylie",

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AB - We define a gradient Ricci soliton to be rigid if it is a flat bundle N ×Γ R{double-struck}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.

KW - Complete manifold

KW - Constant scalar curvature

KW - Einstein manifold

KW - Ricci soliton

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Rigidity of gradient Ricci solitons

Abstract

Keywords

ASJC Scopus subject areas

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