Projective connections associated with second order ODEs
广义相对论与量子宇宙学
2007-05-23 v1
摘要
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".
引用
@article{arxiv.gr-qc/0302016,
title = {Projective connections associated with second order ODEs},
author = {Ezra T Newman and Pawel Nurowski},
journal= {arXiv preprint arXiv:gr-qc/0302016},
year = {2007}
}