Split octonions and generic rank two distributions in dimension five

Katja Sagerschnig

Address.
Institut fuer Mathematik, Universitaet Wien, Nordbergstrasse15, A--1090 Wien, Austria

E-mail.
a9702296@unet.univie.ac.at

Abstract.
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.