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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.17066 |
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| _version_ | 1866913669572460544 |
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| author | Dufour, Jean Paul |
| author_facet | Dufour, Jean Paul |
| contents | Let W be a planar 3-web defined on a neighborhood of a point M. We call "symmetry of W around M" any local diffeomorphism which fixes M and maps each foliation of W to a (not necessarily the same) foliation of W. We say that it is a simple symmetry if it respects each foliation, a mirror symmetry if its respects one foliation and permutes the two other and a circular symmetry if it permutes circularly the three foliations.
Hexagonal (i.e. flat) planar 3-webs have always the three types of symmetry. We study here the non-flat case. We give a classification of 3-webs which admits simple or mirror symmetries. We give a method to build all the 3-webs with a circular symmetry and we exhibit a precise non-flat example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17066 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetries of 3-webs around a point Dufour, Jean Paul Differential Geometry Let W be a planar 3-web defined on a neighborhood of a point M. We call "symmetry of W around M" any local diffeomorphism which fixes M and maps each foliation of W to a (not necessarily the same) foliation of W. We say that it is a simple symmetry if it respects each foliation, a mirror symmetry if its respects one foliation and permutes the two other and a circular symmetry if it permutes circularly the three foliations. Hexagonal (i.e. flat) planar 3-webs have always the three types of symmetry. We study here the non-flat case. We give a classification of 3-webs which admits simple or mirror symmetries. We give a method to build all the 3-webs with a circular symmetry and we exhibit a precise non-flat example. |
| title | Symmetries of 3-webs around a point |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2501.17066 |