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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 and Vojtěch ŽÁDNÍK. Remarks on Grassmannian symmetric spaces. \textit{Archivum Mathematicum}. Brno: Masaryk University, 2008, vol.~44, No~5, p.~569-585. ISSN~0044-8753.
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