Projective connections associated with second order ODEs

Details Projective connections associated with second order ODEs Projective connections associated with second order ODEs

2003-02-05

arxiv.org/abs/gr-qc/0302016v1

Class.Quant.Grav. 20 (2003) 2325-2336

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

We show that every 2nd order ODE defines a 4-parameter family of projective connections on its 2-dimensional solution space. In a special case of ODEs, for which a certain point transformation invariant vanishes, we find that this family of connections always has a preferred representative. This preferred representative turns out to be identical to the projective connection described in Cartan's classic paper "Sur les Varietes a Connection Projective".

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