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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, roč.~42, Supplement, s.~357-368, 11 s. ISSN~1212-5059.
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