Reductions of path structures and classification of homogeneous structures in dimension three
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915602945277952 |
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| author | Falbel, Elisha Mion-Mouton, Martin Veloso, Jose M. |
| author_facet | Falbel, Elisha Mion-Mouton, Martin Veloso, Jose M. |
| contents | In this paper we show that if a path structure has non-vanishing curvature at a point then it has a canonical reduction to a Z/2Z-structure at a neighbourhood of that point (in many cases it has a canonical parallelism). A simple implication of this result is that the automorphism group of a non-flat path structure is of maximal dimension three (a result by Tresse of 1896). We also classify the invariant path structures on three-dimensional Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11509 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reductions of path structures and classification of homogeneous structures in dimension three Falbel, Elisha Mion-Mouton, Martin Veloso, Jose M. Differential Geometry In this paper we show that if a path structure has non-vanishing curvature at a point then it has a canonical reduction to a Z/2Z-structure at a neighbourhood of that point (in many cases it has a canonical parallelism). A simple implication of this result is that the automorphism group of a non-flat path structure is of maximal dimension three (a result by Tresse of 1896). We also classify the invariant path structures on three-dimensional Lie groups. |
| title | Reductions of path structures and classification of homogeneous structures in dimension three |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2406.11509 |