Manifolds with positive curvature operators are space forms

The Ricci flow was introduced by Hamilton in 1982 H1 in order to prove that a compact three-manifold admitting a Riemannian metric of positive Ricci curvature is a spherical space form. In dimension four Hamilton showed that compact four-manifolds with positive curvature operators are spherical space forms as well H2. More generally, the same conclusion holds for compact four-manifolds with 2-positive curvature operators Che. Recall that a curvature operator is called 2-positive, if the sum of its two smallest eigenvalues is positive. In arbitrary dimensions Huisken Hu described an explicit open cone in the space of curvature operators such that the normalized Ricci flow evolves metrics whose curvature operators are contained in that cone into metrics of constant positive sectional curvature.