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Properties and Perturbations of Extremally Ricci-Pinched $G_2$-Structures
We study properties of Extremally Ricci-Pinched (ERP) $G_2$-Structures on compact $7$-manifolds. We provide characterizations of the ERP condition in terms of the traceless $\ast$-Ricci tensor, the Hodge Laplacian of the torsion, the Ricci eigenvalues, the Laplacian flow, and the $27$-dimensional We
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