Classification of complete generic shrinking Ricci solitons with pointwise pinched curvature

摘要

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 (M-n, g, X) is isometric to a finite quotient of R-n or S-n under some pointwise pinched curvature condition. The arguments mainly rely on the Delta(x)-type parabolicity of (M-n,g, X) and algebraic curvature estimates. (C) 2017 Elsevier B.V. All rights reserved.