Jets of flat partial connections
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866909614305443840 |
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| author | Fazoli, Gabriel |
| author_facet | Fazoli, Gabriel |
| contents | We define and study jets of flat partial connections in the setting of smooth foliations and flat partial connections on locally free sheaves. In the case of codimension one foliations, we apply this definition to characterize transversely affine and transversely projective structures. For foliations of arbitrary codimension, we use jets of the Bott connection on the normal sheaf to define the prolongation of a transversely projective structure, and then apply it to produce singular transversely projective structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Jets of flat partial connections Fazoli, Gabriel Complex Variables Differential Geometry 32M10, 32M25, 53C12, 53C30 We define and study jets of flat partial connections in the setting of smooth foliations and flat partial connections on locally free sheaves. In the case of codimension one foliations, we apply this definition to characterize transversely affine and transversely projective structures. For foliations of arbitrary codimension, we use jets of the Bott connection on the normal sheaf to define the prolongation of a transversely projective structure, and then apply it to produce singular transversely projective structures. |
| title | Jets of flat partial connections |
| topic | Complex Variables Differential Geometry 32M10, 32M25, 53C12, 53C30 |
| url | https://arxiv.org/abs/2505.11662 |