On rotationally invariant shrinking gradient Ricci solitons

2007/02/20 by Brett Kotschwar, Kotschwar, Brett
Mathematics · #35K05 #58J35 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:35K05 #msc:58J35

paper · pdf · doi:10.48550/arxiv.math/0702597

14 pages

arxiv created 2007/02/20 · arxiv updated 2009/12/01

Abstract

In this paper we study the gradient Ricci shrinking soliton equation on rotationally symmetric manifolds of dimension three and higher and prove that the only complete examples of such metrics on Sⁿ, \Rn and \R× S^n-1 are, respectively, the round, flat, and standard cylindrical metrics.

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