An upper diameter bound for compact Ricci solitons with application to the Hitchin–Thorpe inequality

Abstract

In this article, stimulated by Fernández-López and García-Río, we shall give an upper diameter bound for compact shrinking Ricci solitons in terms of the range of the scalar curvature, as well as in terms of the range of the potential function. As an application, we shall provide some new sufficient conditions for compact four-dimensional shrinking Ricci solitons to satisfy the Hitchin–Thorpe inequality.