Purely coclosed $\mathrm{G}_2$-structures on nilmanifolds -- II
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912676385390592 |
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| author | Bazzoni, Giovanni Petracci, Giorgia |
| author_facet | Bazzoni, Giovanni Petracci, Giorgia |
| contents | This paper completes the classification of seven-dimensional nilpotent Lie groups endowed with a left-invariant purely coclosed $\text{G}_2$-structure, initiated by the first-named author and collaborators. In this previous work, the authors provided the classification of decomposable seven-dimensional nilpotent Lie groups and of the indecomposable ones up to step $4$ of nilpotency. Here, we address the case of indecomposable $5$- and $6$-step nilpotent Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25511 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Purely coclosed $\mathrm{G}_2$-structures on nilmanifolds -- II Bazzoni, Giovanni Petracci, Giorgia Differential Geometry 53C15, 22E25, 53C38, 17B30 This paper completes the classification of seven-dimensional nilpotent Lie groups endowed with a left-invariant purely coclosed $\text{G}_2$-structure, initiated by the first-named author and collaborators. In this previous work, the authors provided the classification of decomposable seven-dimensional nilpotent Lie groups and of the indecomposable ones up to step $4$ of nilpotency. Here, we address the case of indecomposable $5$- and $6$-step nilpotent Lie groups. |
| title | Purely coclosed $\mathrm{G}_2$-structures on nilmanifolds -- II |
| topic | Differential Geometry 53C15, 22E25, 53C38, 17B30 |
| url | https://arxiv.org/abs/2510.25511 |