The Ricci flow starts with R. Hamilton's famous paper on 3-manifolds with positive Ricci curvature in 1982. In dimension 4, Hamilton proved that the compact 4-manifolds with positive curvature operator are spherical space forms in 1986. More generally, the same result holds for compact 4-manifolds with 2-positive curvature operator by H. Chen in 1991. Recall the curvature operator is called 2-positive if the sum of the 2 smallest eigenvalues is positive. In C. Boehm and B. Wilking's paper, they constructed a new algebraical identity of the curvature operater and then they are able to prove that manifolds with 2-positive operator are space form when the dimension of the manifold is above 2 which generalizes the known results below five.