Tangent groupoid and tangent cones in sub-Riemannian geometry
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866916377877544960 |
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| author | Mohsen, Omar |
| author_facet | Mohsen, Omar |
| contents | Let $X_1,\cdots,X_m$ be vector fields satisfying Hörmander's Lie bracket generating condition on a smooth manifold $M$. We generalise Connes's tangent groupoid, by constructing a completion of the space $M\times M\times \mathbb{R}_+^\times$ using the sub-Riemannian metric. We use our space to calculate all the tangent cones of the sub-Riemannian metric in the sense of the Gromov-Hausdorff distance. This generalises a result of Bellaïche. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_01652 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Tangent groupoid and tangent cones in sub-Riemannian geometry Mohsen, Omar Differential Geometry Metric Geometry Operator Algebras Let $X_1,\cdots,X_m$ be vector fields satisfying Hörmander's Lie bracket generating condition on a smooth manifold $M$. We generalise Connes's tangent groupoid, by constructing a completion of the space $M\times M\times \mathbb{R}_+^\times$ using the sub-Riemannian metric. We use our space to calculate all the tangent cones of the sub-Riemannian metric in the sense of the Gromov-Hausdorff distance. This generalises a result of Bellaïche. |
| title | Tangent groupoid and tangent cones in sub-Riemannian geometry |
| topic | Differential Geometry Metric Geometry Operator Algebras |
| url | https://arxiv.org/abs/2212.01652 |