Canonical connections on sub-Riemannian manifolds with constant symbol
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866917990721650688 |
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| author | Grong, Erlend |
| author_facet | Grong, Erlend |
| contents | As a tool to address the equivalence problem in sub-Riemannian geometry, we introduce a canonical choice of grading and compatible affine connection, available on any sub-Riemannian manifold with constant symbol. We completely compute these structures for contact manifolds of constant symbol, including the cases where the connections of Tanaka-Webster-Tanno are not defined. We also give an original intrinsic grading on sub-Riemannian (2,3,5)-manifolds, and use this to present the first flatness theorem in this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_05366 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Canonical connections on sub-Riemannian manifolds with constant symbol Grong, Erlend Differential Geometry 53C17, 17B70, 58A15 As a tool to address the equivalence problem in sub-Riemannian geometry, we introduce a canonical choice of grading and compatible affine connection, available on any sub-Riemannian manifold with constant symbol. We completely compute these structures for contact manifolds of constant symbol, including the cases where the connections of Tanaka-Webster-Tanno are not defined. We also give an original intrinsic grading on sub-Riemannian (2,3,5)-manifolds, and use this to present the first flatness theorem in this setting. |
| title | Canonical connections on sub-Riemannian manifolds with constant symbol |
| topic | Differential Geometry 53C17, 17B70, 58A15 |
| url | https://arxiv.org/abs/2010.05366 |