Parabolic geometries determined by filtrations of the tangent bundle

Sagerschnig, Katja

Displaying similar documents to “Parabolic geometries determined by filtrations of the tangent bundle”

Remarks on Grassmannian Symmetric Spaces

Lenka Zalabová, Vojtěch Žádník (2008)

Archivum Mathematicum

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The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for $| 1 |$ -graded parabolic geometries and for almost Grassmannian structures, in particular. As an application of two general constructions with parabolic geometries, we present an example of non-flat Grassmannian symmetric space. Next we observe there is a distinguished...

Automorphism groups of parabolic geometries

Čap, Andreas

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Split octonions and generic rank two distributions in dimension five

Katja Sagerschnig (2006)

Archivum Mathematicum

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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.