Efficient construction of contact coordinates for partial prolongations
| dc.creator | Vassiliou, Peter J. | |
| dc.date | 2004-06-11 | |
| dc.date | 2004-07-06 | |
| dc.date.accessioned | 2026-07-07T05:09:10Z | |
| dc.date.available | 2026-07-07T05:09:10Z | |
| dc.description | Let $\CV$ be a vector field distribution on manifold $M$. We give an efficient algorithm for the construction of local coordinates on $M$ such that $\CV$ may be locally expressed as some partial prolongation of the contact distribution $\Cal C^{(1)}_q$, on the first order jet bundle of maps from $\Bbb R$ to $\Bbb R^q$, $q\geq 1$. It is proven that if $\CV$ is locally equivalent to a partial prolongation of $\Cal C^{(1)}_q$ then the explicit construction of contact coordinates algorithmically depends upon the determination of certain first integrals in a sequence of geometrically defined and algorithmically determined integrable Pfaffian systems on $M$. The number of these first integrals that must be computed satisfies a natural minimality criterion. These results therefore provide a full and constructive generalisation of the classical Goursat normal form from the theory of exterior differential systems. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0406234 | |
| dc.identifier | http://arxiv.org/abs/math/0406234 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71531 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58J60; 34H05; 93B18; 93B27 | |
| dc.title | Efficient construction of contact coordinates for partial prolongations | |
| dc.type | text |