On the tightness of left-invariant contact structures
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917455258976256 |
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| author | Bellini, Eugenio |
| author_facet | Bellini, Eugenio |
| contents | We prove that all left-invariant contact structures on three-dimensional Lie groups are tight. The argument is based on Riemannian methods and establishes a unique factorization property for any Lie group admitting a left-invariant contact structure, other than SU(2). We then make use of such factorization property to construct embeddings of left-invariant contact structures into the standard contact structure on $\mathbb R^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06085 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the tightness of left-invariant contact structures Bellini, Eugenio Symplectic Geometry Differential Geometry 22E, 53C, 53D We prove that all left-invariant contact structures on three-dimensional Lie groups are tight. The argument is based on Riemannian methods and establishes a unique factorization property for any Lie group admitting a left-invariant contact structure, other than SU(2). We then make use of such factorization property to construct embeddings of left-invariant contact structures into the standard contact structure on $\mathbb R^3$. |
| title | On the tightness of left-invariant contact structures |
| topic | Symplectic Geometry Differential Geometry 22E, 53C, 53D |
| url | https://arxiv.org/abs/2504.06085 |