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@article{796064,
author = {Zalabová, Lenka},
article_location = {Brno},
article_number = {Supplement},
keywords = {Cartan geometry; parabolic geometry; symmetric space},
language = {eng},
issn = {1212-5059},
journal = {Archivum Mathematicum},
title = {Remarks on symmetries of parabolic geometries},
volume = {42},
year = {2006}
}
TY - JOUR
ID - 796064
AU - Zalabová, Lenka
PY - 2006
TI - Remarks on symmetries of parabolic geometries
JF - Archivum Mathematicum
VL - 42
IS - Supplement
SP - 357-368
EP - 357-368
SN - 12125059
KW - Cartan geometry
KW - parabolic geometry
KW - symmetric space
N2 - 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.
ER -
ZALABOVÁ, Lenka. Remarks on symmetries of parabolic geometries. \textit{Archivum Mathematicum}. Brno, 2006, vol.~42, Supplement, p.~357-368, 11 pp. ISSN~1212-5059.
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