Existence and classification of the Cartan $(2,3,5)$-distribution
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917057756397568 |
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| author | Adachi, Jiro |
| author_facet | Adachi, Jiro |
| contents | The Cartan $(2,3,5)$-distribution is a tangent distribution of rank~$2$ on a $5$-dimensional manifold satisfying certain generic conditions. The necessary and sufficient condition for a manifold to admit such a structure is established in this paper. The condition obtained is purely topological. In addition, the classification of such structures, up to homotopy as formal Cartan distributions, is obtained. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_01890 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and classification of the Cartan $(2,3,5)$-distribution Adachi, Jiro Differential Geometry Geometric Topology 53C15, 58A30, 57R45 The Cartan $(2,3,5)$-distribution is a tangent distribution of rank~$2$ on a $5$-dimensional manifold satisfying certain generic conditions. The necessary and sufficient condition for a manifold to admit such a structure is established in this paper. The condition obtained is purely topological. In addition, the classification of such structures, up to homotopy as formal Cartan distributions, is obtained. |
| title | Existence and classification of the Cartan $(2,3,5)$-distribution |
| topic | Differential Geometry Geometric Topology 53C15, 58A30, 57R45 |
| url | https://arxiv.org/abs/2511.01890 |