01291nas a2200145 4500008004100000245005300041210005000094260002500144300001600169490000700185520083300192100002001025700001701045856008301062 2012 eng d00aOn Galilean connections and the first jet bundle0 aGalilean connections and the first jet bundle bSpringerc2012/10/01 a1889–18950 v103 aWe 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.1 aDE Grant, James1 aLackey, Brad uhttps://quics.umd.edu/publications/galilean-connections-and-first-jet-bundle-0