%0 Journal Article
%J Central European Journal of Mathematics
%D 2012
%T On Galilean connections and the first jet bundle
%A Grant, James DE
%A Brad Lackey
%X 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.
%B Central European Journal of Mathematics
%I Springer
%V 10
%P 1889–1895
%8 2012/10/01
%G eng