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.
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 
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/
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     zbl = {1164.53362},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2006_42_5_a19/}
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