TY - JOUR
T1 - On Galilean connections and the first jet bundle
Y1 - 1999
A1 - James D. E. Grant
A1 - Brad Lackey
AB - We express the first jet bundle of curves in Euclidean space as homogeneous spaces associated to a Galilean-type group. Certain Cartan connections on a manifold with values in the Lie algebra of the Galilean group are characterized as geometries associated to systems of second order ordinary differential equations. We show these Cartan connections admit a form of normal coordinates, and that in these normal coordinates the geodesic equations of the connection are second order ordinary differential equations. We then classify such connections by some of their torsions, extending a classical theorem of Chern involving the geometry associated to a system of second order differential equations.
UR - http://arxiv.org/abs/math/9909148v1
J1 - Central European Journal of Mathematics 10.5 (2012): 1889-1895
ER -