Geodesic
Split octonions and generic rank two distributions in dimension five
Archivum mathematicum, Tome 42 (2006) no. 5, pp. 329-339

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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.
Classification : 53C30, 58A30 
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     author = {Sagerschnig, Katja},
     title = {Split octonions and generic rank two distributions in dimension five},
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Sagerschnig, Katja. Split octonions and generic rank two distributions in dimension five. Archivum mathematicum, Tome 42 (2006) no. 5, pp. 329-339. http://geodesic.mathdoc.fr/item/ARM_2006__42_5_a19/