Year: 2026
Type: preprint
Abstract: 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 Einstein or isometrically covered by $\mathbb{S}^{1}\times\mathbb{S}^{n-1}(κ)$ endowed with the product metric.
Source: arXiv (Cornell University)
Institution: Universidade Federal de Pernambuco
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G3383999570
OpenAlex ID: W7169860652
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