Steady Ricci solitons with horizontally ε-pinched Ricci curvature

In this paper,we prove that anyκ-noncollapsed gradient steady Ricci soliton with nonnegative curvature operator and horizontallyκ-pinched Ricci curvature must be rotationally symmetric.As an application,we show that anyκ-noncollapsed gradient steady Ricci soliton(Mn,g,f)with nonnegative curvature operator must be rotationally symmetric if it admits a unique equilibrium point and its scalar curvature R(x)satisfies lim_(ρ(x)→∞)R(x)f(x)=C_(0)sup_(x∈M)R(x)with C_(0)>n-2/2.