Prolongations of $(3, 6)$-distributions by singular curves
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914487888510976 |
|---|---|
| author | Ishikawa, Goo Machida, Yoshinori |
| author_facet | Ishikawa, Goo Machida, Yoshinori |
| contents | A subbundle of rank 3 in the tangent bundle over a 6-dimensional manifold is called a (3, 6)-distribution if its local sections generate the whole tangent bundle by taking their Lie brackets once. An integral curve of a distribution, whose velocity vectors belong to the distribution, can be a singular curve or an abnormal extremal in the sense of geometric control theory. In this paper, given a (3, 6)-distribution, we prolong it, using the data of singular curves, to a (3,5,7,8)-distribution, to a (3, 5, 7, 8, 9)-distribution which possesses additional pseudo-product structure respectively. Regarding also another prolongation to a (4, 6, 8)-distribution, we show the equivalence of the classification problems of those four classes of distributions obtained from (3, 6)-distributions, generalising the correspondences of those in B_3-SO(3,4)-homogeneous models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10507 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Prolongations of $(3, 6)$-distributions by singular curves Ishikawa, Goo Machida, Yoshinori Differential Geometry Primary 58A30, Secondary 53C17, 53B30, 58C25, 58E10, 70H05, 93B27 A subbundle of rank 3 in the tangent bundle over a 6-dimensional manifold is called a (3, 6)-distribution if its local sections generate the whole tangent bundle by taking their Lie brackets once. An integral curve of a distribution, whose velocity vectors belong to the distribution, can be a singular curve or an abnormal extremal in the sense of geometric control theory. In this paper, given a (3, 6)-distribution, we prolong it, using the data of singular curves, to a (3,5,7,8)-distribution, to a (3, 5, 7, 8, 9)-distribution which possesses additional pseudo-product structure respectively. Regarding also another prolongation to a (4, 6, 8)-distribution, we show the equivalence of the classification problems of those four classes of distributions obtained from (3, 6)-distributions, generalising the correspondences of those in B_3-SO(3,4)-homogeneous models. |
| title | Prolongations of $(3, 6)$-distributions by singular curves |
| topic | Differential Geometry Primary 58A30, Secondary 53C17, 53B30, 58C25, 58E10, 70H05, 93B27 |
| url | https://arxiv.org/abs/2602.10507 |