2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124356In 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 $S^n$, $\R{n}$ and $\R{}\times S^{n-1}$ are, respectively, the round, flat, and standard cylindrical metrics.14 pagesDifferential GeometryAnalysis of PDEs58J35; 35K05text