Isolated singularities in $G_2$-structures with torsion
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908901069291520 |
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| author | Earp, Henrique Sá Stein, Jakob |
| author_facet | Earp, Henrique Sá Stein, Jakob |
| contents | We revisit the study of $G_2$-structures with special torsion, and isolated singularities. Many of the known examples with conical singularities admit additional symmetries, and we describe circle-invariant $G_2$-structures in this context. Finally, we show that collapsing the circle fibres of a contact Calabi-Yau manifold at isolated points cannot produce a $G_2$-structure with bounded torsion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15482 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isolated singularities in $G_2$-structures with torsion Earp, Henrique Sá Stein, Jakob Differential Geometry 53C25, 53C10 We revisit the study of $G_2$-structures with special torsion, and isolated singularities. Many of the known examples with conical singularities admit additional symmetries, and we describe circle-invariant $G_2$-structures in this context. Finally, we show that collapsing the circle fibres of a contact Calabi-Yau manifold at isolated points cannot produce a $G_2$-structure with bounded torsion. |
| title | Isolated singularities in $G_2$-structures with torsion |
| topic | Differential Geometry 53C25, 53C10 |
| url | https://arxiv.org/abs/2506.15482 |