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arXiv · 0710.3174

Rigidity of gradient Ricci Solitons

Peter Petersen·William Wylie
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Abstract

We define a gradient Ricci soliton to be rigid if it is a flat bundle $% N\times_Γ\mathbb{R}^{k}$ 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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Peter Petersen, William Wylie. 2007-10-16. Rigidity of gradient Ricci Solitons. https://arxiv.org/abs/0710.3174

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