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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2510.25918 |
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| _version_ | 1866917140489043968 |
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| author | Ashley, Brandon P. Schultz, Michael T. |
| author_facet | Ashley, Brandon P. Schultz, Michael T. |
| contents | We study geometric aspects of horizontal 2-plane distributions on the complement of the zero section in the 5-dimensional total space of a rank-3 vector bundle equipped with connection over a surface. We show that any surface in 3-dimensional projective space can be associated to such a geometric structure in 5-dimensions, and establish a dictionary between the projective differential geometry of the surface and the growth vector of the 2-plane distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25918 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric aspects of rank-3 vector bundles over surfaces and 2-plane distributions on 5-manifolds Ashley, Brandon P. Schultz, Michael T. Differential Geometry 35A30, 53A20, 53B15 We study geometric aspects of horizontal 2-plane distributions on the complement of the zero section in the 5-dimensional total space of a rank-3 vector bundle equipped with connection over a surface. We show that any surface in 3-dimensional projective space can be associated to such a geometric structure in 5-dimensions, and establish a dictionary between the projective differential geometry of the surface and the growth vector of the 2-plane distribution. |
| title | Geometric aspects of rank-3 vector bundles over surfaces and 2-plane distributions on 5-manifolds |
| topic | Differential Geometry 35A30, 53A20, 53B15 |
| url | https://arxiv.org/abs/2510.25918 |