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PreprintCC BY 4.0arXiv

Properties and Perturbations of Extremally Ricci-Pinched G2-Structures

  • Aaron Kennon
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Abstract

We study properties of Extremally Ricci-Pinched (ERP) G2-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 G2-Structure is finite. We then identify perturbations of ERP G2-Structures, both in general and for specific examples, that preserve the ERP condition.

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Cite

BibTeXRIS
BibTeX
@misc{kennon2026properties,
  title = {{Properties and Perturbations of Extremally Ricci-Pinched $G_2$-Structures}},
  author = {Aaron Kennon},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34154},
  eprint = {2609.34154},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34154},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Properties and Perturbations of Extremally Ricci-Pinched G_2-Structures
AU  - Aaron Kennon
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34154
UR  - https://arxiv.org/abs/2609.34154
AB  - 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.
ER  -