Publication details

Remarks on Grassmannian symmetric spaces

Authors

ZALABOVÁ Lenka ŽÁDNÍK Vojtěch

Year of publication 2008
Type Article in Periodical
Magazine / Source Archivum Mathematicum
MU Faculty or unit

Faculty of Education

Citation
Web
Field General mathematics
Keywords parabolic geometries; Weyl structures; almost Grassmannian structures; symmetric spaces
Description 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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info