2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215164We apply an equivariant version of Perelman's Ricci flow with surgery to study smooth actions by finite groups on closed 3-manifolds. Our main result is that such actions on elliptic and hyperbolic 3-manifolds are conjugate to isometric actions. Combining our results with results by Meeks and Scott [17], it follows that such actions on geometric 3-manifolds (in the sense of Thurston) are always geometric, i.e. there exist invariant locally homogeneous Riemannian metrics. This answers a question posed by Thurston in [32].36 pages. Final version, to appear in Geometry & Topology. Main Theorem extended to actions on hyperbolic 3-manifolds with cuspsGeometric TopologyDifferential Geometry57M60, 57M50 (Primary) 53C21, 53C44 (Secondary)text