Abstract
In this article, we first derive several identities on a compact shrinking Ricci soliton. We then show that a compact gradient shrinking soliton must be Einstein, if it admits a Riemannian metric with positive curvature operator and satisfies an integral inequality. Furthermore, such a soliton must be of constant curvature.
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Cao, X. Compact gradient shrinking Ricci solitons with positive curvature operator. J Geom Anal 17, 425–433 (2007). https://doi.org/10.1007/BF02922090
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DOI: https://doi.org/10.1007/BF02922090