Rigidity of gradient Ricci Solitons

Abstract

We define a gradient Ricci soliton to be rigid if it is a flat bundle 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.

16 pages

References in corpus (1)

• Some Geometry and Analysis on Ricci Solitons

Cited by in corpus (1)

• On gradient Ricci solitons with Symmetry