Abstract
Stimulated by improved oscillation estimates of the potential function and the scalar curvature on compact gradient Ricci solitons introduced in a recent study by Cheng, Ribeiro, and Zhou [Proc. Am. Math. Soc. Ser. B 10, 33–45 (2023)], we give several new sufficient conditions for compact four-dimensional normalized shrinking Ricci solitons to satisfy the Hitchin–Thorpe inequality. Our new conditions refine the validity of the Hitchin–Thorpe inequality obtained by Tadano [J. Math. Phys. 58, 023503 (2017)], Tadano [J. Math. Phys. 59, 043507 (2018)], and Tadano [Differ. Geom. Appl. 66, 231–241 (2019)].
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