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An integral inequality for compact Bach-flat $\mathcal{A}_{2}$-manifolds
We establish a Catino-type integral inequality for closed Bach-flat $\mathcal{A}_2$-manifolds, namely Riemannian manifolds with nonnegative scalar curvature and constant nonnegative second Schouten curvature. In the equality case, we derive rigidity results showing that the manifold is either Einste
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