Publication details

Remarks on symmetries of parabolic geometries



Year of publication 2006
Type Article in Periodical
Magazine / Source Archivum Mathematicum
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Cartan geometry; parabolic geometry; symmetric space
Description We consider symmetries on filtered manifolds and we study the $|1|$-graded parabolic geometries in more details. We discuss the existence of symmetries on the homogeneous models and we conclude some observations on the general curved geometries. In particular, the existence of an symmetry at a point kills the torsion of the geometry at this point. In view of the nice general theory of parabolic geometries, this already proves the local flatness of the symmetric geometries for most types of them.
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