Isolated singularities in G₂-structures with torsion

We revisit the study of G₂ G 2 -structures with special torsion, and isolated singularities. Many of the known examples with conical singularities admit additional symmetries, and we describe circle-invariant G₂ G 2 -structures in this context. Finally, we show that collapsing the circle fibres of a contact Calabi-Yau manifold at isolated points cannot produce a G₂ G 2 -structure with bounded torsion.