FOUR-MANIFOLDS WITH 1/4-PINCHED FLAG CURVATURES ∗

The Ricci flow on a compact four-manifold preserves the condition of pointwise 1/4- pinching of flag curvatures. Any compact Riemannian four-manifold with 1/4-pinched flag curvatures is either isometric to CP 2 or diffeomorphic to a space-form.