Complete non-compact gradient Ricci solitons with nonnegative Ricci curvature

Abstract

In this paper, we give a delay estimate of scalar curvature for a complete non-compact expanding (or steady) gradient Ricci soliton with nonnegative Ricci curvature. As an application, we prove that any complete non-compact expanding (or steady) gradient Kähler-Ricci solitons with positively pinched Ricci curvature should be Ricci flat. The result answers a question in case of Kähler-Ricci solitons proposed by Chow, Lu and Ni in a book.

18 pages

References in corpus (4)

• Ricci flow with surgery on three-manifolds
• An optimal gap theorem
• On the simply connectedness of non-negatively curved Kähler manifolds and applications
• Gradient Kähler-Ricci solitons and a uniformization conjecture