On Galilean connections and the first jet bundle
- Author(s)
- James Grant, Bradley C. Lackey
- Abstract
We see how the first jet bundle of curves into affine space can be realized as a homogeneous space of the Galilean group. Cartan connections with this model are precisely the geometric structure of second-order ordinary differential equations under time-preserving transformations - sometimes called KCC-theory. With certain regularity conditions, we show that any such Cartan connection induces "laboratory" coordinate systems, and the geodesic equations in this coordinates form a system of second-order ordinary differential equations. We then show the converse - the "fundamental theorem" - that given such a coordinate system, and a system of second order ordinary differential equations, there exists regular Cartan connections yielding these, and such connections are completely determined by their torsion.
- Organisation(s)
- Gravitational Physics
- External organisation(s)
- National Security Agency
- Journal
- Central European Journal of Mathematics
- Volume
- 10
- Pages
- 1889-1895
- No. of pages
- 7
- ISSN
- 1895-1074
- DOI
- https://doi.org/10.2478/s11533-012-0089-4
- Publication date
- 2012
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103019 Mathematical physics
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/on-galilean-connections-and-the-first-jet-bundle(772d7a34-a6ea-43e1-a687-de6e1591ad93).html