Contact Path Geometries
| dc.creator | Fox, Daniel J. F. | |
| dc.date | 2005-08-18 | |
| dc.date.accessioned | 2026-07-07T05:22:28Z | |
| dc.date.available | 2026-07-07T05:22:28Z | |
| dc.description | Contact path geometries are curved geometric structures on a contact manifold comprising smooth families of paths modeled on the family of all isotropic lines in the projectivization of a symplectic vector space. Locally such a structure is equivalent to the graphs in the space of independent and depedent variables of the family of solutions of a system of an odd number of second order ODE's subject to a single maximally non-integrable constraint. A subclass of contact path geometries is distinguished by the vanishing of an invariant contact torsion. For this subclass the equivalence problem is solved by constructing a normalized Cartan connection using the methods of Tanaka-Morimoto-Čap-Schichl. The geometric meaning of the contact torsion is described. If a secondary contact torsion vanishes then the locally defined space of contact paths admits a split quaternionic contact structure (analogous to the quaternionic contact structures studied by O. Biquard). | |
| dc.description | 36 pages | |
| dc.identifier | https://arxiv.org/abs/math/0508343 | |
| dc.identifier | http://arxiv.org/abs/math/0508343 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76072 | |
| dc.subject | Differential Geometry | |
| dc.subject | 32L25; 53A55 | |
| dc.title | Contact Path Geometries | |
| dc.type | text |