Mathematics > Differential Geometry
[Submitted on 16 Oct 2007]
Title:Rigidity of gradient Ricci Solitons
View PDFAbstract: We define a gradient Ricci soliton to be rigid if it is a flat bundle $% N\times_{\Gamma}\mathbb{R}^{k}$ 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.
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