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Split octonions and generic rank two distributions in dimension five. (English) Zbl 1164.53362
Summary: 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.

##### MSC:
 53C30 Differential geometry of homogeneous manifolds 58A30 Vector distributions (subbundles of the tangent bundles)
##### Keywords:
octonions; Cartan geometry; homogeneous model
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