Classification of complete generic shrinking Ricci solitons with pointwise pinched curvature

The purpose of this paper is to investigate complete generic shrinking Ricci solitons with pointwise pinched curvature and prove two classification results for such manifolds. In particular, we show that any n-dimensional generic shrinking Ricci soliton (Mn,g,X) is isometric to a finite quotient of Rn or Sn under some pointwise pinched curvature condition. The arguments mainly rely on the ΔX-type parabolicity of (Mn,g,X) and algebraic curvature estimates.