Properties and Perturbations of Extremally Ricci-Pinched $G_2$-Structures

Aaron Kennon

paper

Properties and Perturbations of Extremally Ricci-Pinched $G_{2}$ -Structures

arXiv:2609.34154

Abstract

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 $*$ -Ricci tensor, the Hodge Laplacian of the torsion, the Ricci eigenvalues, the Laplacian flow, and the $27$ -dimensional Weyl curvature component. We also prove that the automorphism group of a compact ERP $G_{2}$ -Structure is finite. We then identify perturbations of ERP $G_{2}$ -Structures, both in general and for specific examples, that preserve the ERP condition.

arXiv comment17 pages

Properties and Perturbations of Extremally Ricci-Pinched G2​-Structures

Abstract

Properties and Perturbations of Extremally Ricci-Pinched $G_{2}$ -Structures