Remarks on Grassmannian Symmetric Spaces

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dc.creatorZalabova, Lenka
dc.creatorZadnik, Vojtech
dc.date2009-01-07
dc.date.accessioned2026-07-07T13:17:25Z
dc.date.available2026-07-07T13:17:25Z
dc.descriptionThe 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 torsion--free affine connection preserving the Grassmannian structure so that, with respect to this connection, the Grassmannian symmetric space is an affine symmetric space in the classical sense.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/0901.0777
dc.identifierhttp://arxiv.org/abs/0901.0777
dc.identifierArchivum Mathematicum, Vol. 44 (2008), No. 5, 569-585
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/231106
dc.subjectDifferential Geometry
dc.subject53C15; 53A40; 53C05; 53C35
dc.titleRemarks on Grassmannian Symmetric Spaces
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