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In this article, stimulated by Fernandez-Lopez and Garcia-Rio, we shall givean upper diameter bound for compact Ricci solitons in terms of the range of thescalar curvature. As an application, we shall provide some sufficientconditions for four-dimensional compact Ricci solitons to satisfy theHitchin-Thorpe inequality.

An upper diameter bound for compact Ricci solitons with applications to the Hitchin-Thorpe inequality