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Title: | Remarks on Grassmannian symmetric spaces | ||||||||||
Author: | Zalabová, Lenka; Žádník, Vojtěch | ||||||||||
Document type: | Peer-reviewed article (English) | ||||||||||
Source document: | Archivum Mathematicum. 2008, vol. 44, issue 5, p. 569-585 | ||||||||||
ISSN: | 0044-8753 (Sherpa/RoMEO, JCR) | ||||||||||
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Abstract: | 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 |l|-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-fat 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. | ||||||||||
Full text: | http://www.maths.soton.ac.uk/EMIS/journals/AM/08-5/index.html | ||||||||||
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