On Galilean connections and the first jet bundle

• Autorzy: James Grant , Bradley Lackey
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Galilean group; Cartan connections; Jet bundles; 2nd order ODE

Kategorie tematyczne

• 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
• 70G45: Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.)
• 58A20: Jets

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 5
• Strony: 1889-1895

Daty

wydano

2012-10-01

online

2012-07-24

Twórcy

autor

James Grant

• Universität Wien

autor

Bradley Lackey

• National Security Agency

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0089-4