Compact Gradient Shrinking Ricci Solitons with Positive Curvature   Operator
  In this paper, we study the following conjecture of Hamilton: Any compact gradient shrinking Ricci soliton with positive curvature operator must be Einstein. We first derive several identities. Then we show that the conjecture is true under an additional condition. Furthermore, such a soliton must be of constant curvature. 
Xiaodong Cao