Geometry of a pair of second-order ODEs and Euclidean spaces
| dc.creator | Atkins, Richard | |
| dc.date | 2006-10-02 | |
| dc.date.accessioned | 2026-07-07T07:28:36Z | |
| dc.date.available | 2026-07-07T07:28:36Z | |
| dc.description | This paper investigates the relationship between a system of differential equations and the underlying geometry associated with it. The geometry of a surface determines shortest paths, or geodesics connecting nearby points, which are defined as the solutions to a pair of second-order differential equations: the Euler-Lagrange equations of the arclength action. We ask when the converse holds, that is, when solutions to a system of differential equations reveals an underlying geometry. Specifically, when may the solutions to a pair of second-order ordinary differential equations be reparameterized so as to give, locally, the geodesics of a Euclidean space? Our approach is based upon Cartan's method of equivalence. In the second part of the paper, the equivalence problem is solved for a generic pair of second-order ODEs revealing the existence of 24 invariant functions. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610082 | |
| dc.identifier | http://arxiv.org/abs/math/0610082 | |
| dc.identifier | Canad. Math. Bull. Vol. 49 (2), 2006 pp. 170-184 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117794 | |
| dc.subject | Differential Geometry | |
| dc.title | Geometry of a pair of second-order ODEs and Euclidean spaces | |
| dc.type | text |