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We apply an equivariant version of Perelman's Ricci flow with surgery tostudy smooth actions by finite groups on closed 3-manifolds. Our main result isthat such actions on elliptic and hyperbolic 3-manifolds are conjugate toisometric actions. Combining our results with results by Meeks and Scott [17],it follows that such actions on geometric 3-manifolds (in the sense ofThurston) are always geometric, i.e. there exist invariant locally homogeneousRiemannian metrics. This answers a question posed by Thurston in [32].

Equivariant Ricci flow with surgery and applications to finite group actions on geometric 3–manifolds