We define a gradient Ricci soliton to be rigid if it is a flat bundle N*GammaRk 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.
Petersen, Peter and Wylie, William, "Rigidity of Gradient Ricci Solitons" (2007). Mathematics Faculty Scholarship. Paper 127.
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