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@article{816214, author = {Zalabová, Lenka and Žádník, Vojtěch}, article_location = {Brno}, article_number = {5}, keywords = {parabolic geometries; Weyl structures; almost Grassmannian structures; symmetric spaces}, language = {eng}, issn = {0044-8753}, journal = {Archivum Mathematicum}, title = {Remarks on Grassmannian symmetric spaces}, url = {http://emis.muni.cz/journals/AM/08-5/}, volume = {44}, year = {2008} }
TY - JOUR ID - 816214 AU - Zalabová, Lenka - Žádník, Vojtěch PY - 2008 TI - Remarks on Grassmannian symmetric spaces JF - Archivum Mathematicum VL - 44 IS - 5 SP - 569-585 EP - 569-585 PB - Masaryk University SN - 00448753 KW - parabolic geometries KW - Weyl structures KW - almost Grassmannian structures KW - symmetric spaces UR - http://emis.muni.cz/journals/AM/08-5/ N2 - 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 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. ER -
ZALABOVÁ, Lenka a Vojtěch ŽÁDNÍK. Remarks on Grassmannian symmetric spaces. \textit{Archivum Mathematicum}. Brno: Masaryk University, 2008, roč.~44, č.~5, s.~569-585. ISSN~0044-8753.
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