# On Galilean connections and the first jet bundle

Open Mathematics (2012)

- Volume: 10, Issue: 5, page 1889-1895
- ISSN: 2391-5455

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topJames Grant, and Bradley Lackey. "On Galilean connections and the first jet bundle." Open Mathematics 10.5 (2012): 1889-1895. <http://eudml.org/doc/269376>.

@article{JamesGrant2012,

abstract = {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.},

author = {James Grant, Bradley Lackey},

journal = {Open Mathematics},

keywords = {Galilean group; Cartan connections; Jet bundles; 2nd order ODE; jet bundles},

language = {eng},

number = {5},

pages = {1889-1895},

title = {On Galilean connections and the first jet bundle},

url = {http://eudml.org/doc/269376},

volume = {10},

year = {2012},

}

TY - JOUR

AU - James Grant

AU - Bradley Lackey

TI - On Galilean connections and the first jet bundle

JO - Open Mathematics

PY - 2012

VL - 10

IS - 5

SP - 1889

EP - 1895

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.

LA - eng

KW - Galilean group; Cartan connections; Jet bundles; 2nd order ODE; jet bundles

UR - http://eudml.org/doc/269376

ER -

## References

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