Some rigidity results for noncompact gradient steady Ricci solitons and Ricci-flat manifolds

Abstract

Abstract. Gradient steady Ricci solitons are natural generalizations of Ricciflat manifolds. In this article, we prove a curvature gap theorem for gradient steady Ricci solitons with nonconstant potential functions; and a curvature gap theorem for Ricci-flat manifolds, removing the volume growth assumptions in known results.