Abstract

We define a gradient Ricci soliton to be rigid if it is a flat bundle N ×_ΓR^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, Ricci soliton, Einstein manifold

Mathematical Subject Classification

Primary: 53C25

Milestones

Received: 3 December 2008
Accepted: 15 December 2008

Authors