Two Fefferman-type constructions involving almost Grassmann structures and path geometries
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914529330331648 |
|---|---|
| author | Guo, Zhangwen |
| author_facet | Guo, Zhangwen |
| contents | We introduce a Fefferman-type construction that associates an almost Grassmannian structure of type $(2,n+1)$ to every $(n+1)$-dimensional path geometry. We prove that the construction is normal and provide two equivalent characterizing conditions for all almost Grassmannian structures which locally arise from this construction: one in terms of certain parallel tractors and the other in terms of a Weyl connection of an almost Grassmann structure. We prove that the latter condition is independent of the choice of Weyl connection.
We then introduce a related Fefferman-type construction associating an almost Grassmannian structure of type $(2,n+1)$ to every almost Grassmannian structure of type $(2,n)$. We prove that this construction is non-normal and characterize all almost Grassmannian structures which locally arise in this way in Cartan geometric terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04878 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two Fefferman-type constructions involving almost Grassmann structures and path geometries Guo, Zhangwen Differential Geometry We introduce a Fefferman-type construction that associates an almost Grassmannian structure of type $(2,n+1)$ to every $(n+1)$-dimensional path geometry. We prove that the construction is normal and provide two equivalent characterizing conditions for all almost Grassmannian structures which locally arise from this construction: one in terms of certain parallel tractors and the other in terms of a Weyl connection of an almost Grassmann structure. We prove that the latter condition is independent of the choice of Weyl connection. We then introduce a related Fefferman-type construction associating an almost Grassmannian structure of type $(2,n+1)$ to every almost Grassmannian structure of type $(2,n)$. We prove that this construction is non-normal and characterize all almost Grassmannian structures which locally arise in this way in Cartan geometric terms. |
| title | Two Fefferman-type constructions involving almost Grassmann structures and path geometries |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2509.04878 |