Geodesic
Remarks on Grassmannian Symmetric Spaces
Archivum mathematicum, Tome 44 (2008) no. 5, pp. 569-585.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 53A40, 53C05, 53C15, 53C35
Keywords: parabolic geometries; Weyl structures; almost Grassmannian structures; symmetric spaces 
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     author = {Zalabov\'a, Lenka and \v{Z}\'adn{\'\i}k, Vojt\v{e}ch},
     title = {Remarks on {Grassmannian} {Symmetric} {Spaces}},
     journal = {Archivum mathematicum},
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     zbl = {1212.53054},
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Zalabová, Lenka; Žádník, Vojtěch. Remarks on Grassmannian Symmetric Spaces. Archivum mathematicum, Tome 44 (2008) no. 5, pp. 569-585. http://geodesic.mathdoc.fr/item/ARM_2008__44_5_a15/