In his famous five variables paper Elie Cartan showed that one can canonically associate to a generic rank 2 distribution on a 5 dimensional manifold a Cartan geometry modeled on the homogeneous space $\tilde{G}_2/P$, where $P$ is one of the maximal parabolic subgroups of the exceptional Lie group $\tilde{G}_2$. In this article, we use the algebra of split octonions to give an explicit global description of the distribution corresponding to the homogeneous model.
@article{108039,
author = {Katja Sagerschnig},
title = {Split octonions and generic rank two distributions in dimension five},
journal = {Archivum Mathematicum},
volume = {042},
year = {2006},
pages = {329-339},
zbl = {1164.53362},
mrnumber = {2322419},
language = {en},
url = {http://dml.mathdoc.fr/item/108039}
}
Sagerschnig, Katja. Split octonions and generic rank two distributions in dimension five. Archivum Mathematicum, Tome 042 (2006) pp. 329-339. http://gdmltest.u-ga.fr/item/108039/
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