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On Galilean connections and the first jet bundle

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Grant J., Lackey B.

Open Mathematics

2012

tom 10

nr 5

1889-1895

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.

Ograniczanie wyników

1 Open Mathematics

1 Grant J.

1 Lackey B.

1 2012

Wyniki wyszukiwania

On Galilean connections and the first jet bundle