Isolated singularities in $G_2$-structures with torsion
Differential Geometry
2026-03-20 v2
Abstract
We revisit the study of -structures with special torsion, and isolated singularities. Many of the known examples with conical singularities admit additional symmetries, and we describe circle-invariant -structures in this context. Finally, we show that collapsing the circle fibres of a contact Calabi-Yau manifold at isolated points cannot produce a -structure with bounded torsion.
Keywords
Cite
@article{arxiv.2506.15482,
title = {Isolated singularities in $G_2$-structures with torsion},
author = {Henrique Sá Earp and Jakob Stein},
journal= {arXiv preprint arXiv:2506.15482},
year = {2026}
}
Comments
12 pages. v2: exposition expanded, more proofs added. Many typos corrected throughout, and corrected formula appearing in Proposition 13. To appear in Geometriae Dedicata