01069nas a2200121 4500008004100000245005300041210005000094260001500144520070700159100002400866700001700890856004000907 1999 eng d00aOn Galilean connections and the first jet bundle0 aGalilean connections and the first jet bundle c1999/09/243 a 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.
1 aGrant, James, D. E.1 aLackey, Brad uhttp://arxiv.org/abs/math/9909148v1