$C^1$-Local Flatness and Geodesics of the Legendrian Spectral Distance
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909138303320064 |
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| author | Allais, Simon Arlove, Pierre-Alexandre |
| author_facet | Allais, Simon Arlove, Pierre-Alexandre |
| contents | In this article, we give an explicit computation of the order spectral selectors of a pair of $C^1$-close Legendrian submanifolds belonging to an orderable isotopy class. The $C^1$-local flatness of the spectral distance and the characterisation of its geodesics are deduced. Another consequence is the $C^1$-local coincidence of spectral and Shelukhin-Chekanov-Hofer distances. Similar statements are then deduced for several contactomorphism groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10679 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $C^1$-Local Flatness and Geodesics of the Legendrian Spectral Distance Allais, Simon Arlove, Pierre-Alexandre Symplectic Geometry 53D10, 57R17, 58B20 In this article, we give an explicit computation of the order spectral selectors of a pair of $C^1$-close Legendrian submanifolds belonging to an orderable isotopy class. The $C^1$-local flatness of the spectral distance and the characterisation of its geodesics are deduced. Another consequence is the $C^1$-local coincidence of spectral and Shelukhin-Chekanov-Hofer distances. Similar statements are then deduced for several contactomorphism groups. |
| title | $C^1$-Local Flatness and Geodesics of the Legendrian Spectral Distance |
| topic | Symplectic Geometry 53D10, 57R17, 58B20 |
| url | https://arxiv.org/abs/2403.10679 |