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Displaying similar documents to “Split octonions and generic rank two distributions in dimension five”

Parabolic geometries determined by filtrations of the tangent bundle

Sagerschnig, Katja

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Summary: Let 𝔤 be a real semisimple | k | -graded Lie algebra such that the Lie algebra cohomology group H 1 ( 𝔤 - , 𝔤 ) is contained in negative homogeneous degrees. We show that if we choose G = Aut ( 𝔤 ) and denote by P the parabolic subgroup determined by the grading, there is an equivalence between regular, normal parabolic geometries of type ( G , P ) and filtrations of the tangent bundle, such that each symbol algebra gr ( T x M ) is isomorphic to the graded Lie algebra 𝔤 - . Examples of parabolic geometries determined by filtrations...

Free CR distributions

Gerd Schmalz, Jan Slovák (2012)

Open Mathematics

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There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions n and codimensions n 2 are among the very few possibilities of the so-called parabolic geometries. Indeed, the homogeneous model turns out to be PSU(n+1,n)/P with a suitable parabolic subgroup P. We study the geometric properties of such real (2n+n 2)-dimensional submanifolds in ℂ n + n 2 for all n...