On Galilean connections and the first jet bundle

Autor(en)

James Grant, Bradley C. Lackey

Abstrakt

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(en)

Gravitationsphysik

Externe Organisation(en)

National Security Agency

Journal

Central European Journal of Mathematics

Band

10

Seiten

1889-1895

Anzahl der Seiten

7

ISSN

1895-1074

DOI

https://doi.org/10.2478/s11533-012-0089-4

Publikationsdatum

2012

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/772d7a34-a6ea-43e1-a687-de6e1591ad93