# Rigidity of gradient Ricci Solitons - Mathematics > Differential Geometry

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Abstract: 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 allgradient solitons are rigid. Here we offer several natural conditions on thecurvature that characterize rigid gradient solitons. Other related results onrigidity of Ricci solitons are also explained in the last section.

Autor: Peter Petersen, William Wylie

Fuente: https://arxiv.org/