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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.

53C30 Differential geometry of homogeneous manifolds
58A30 Vector distributions (subbundles of the tangent bundles)
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