TY - JOUR
T1 - On Galilean connections and the first jet bundle
JF - Central European Journal of Mathematics
Y1 - 2012
A1 - Grant, James DE
A1 - Brad Lackey
AB - 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.
PB - Springer
VL - 10
U4 - 1889–1895
ER -