ZALABOVÁ, Lenka. Remarks on symmetries of parabolic geometries. Archivum Mathematicum. Brno, 2006, vol. 42, Supplement, p. 357-368, 11 pp. ISSN 1212-5059.
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Basic information
Original name Remarks on symmetries of parabolic geometries
Name in Czech Poznámky k symetriím parabolických geometrií
Authors ZALABOVÁ, Lenka (203 Czech Republic, guarantor).
Edition Archivum Mathematicum, Brno, 2006, 1212-5059.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher Czech Republic
Confidentiality degree is not subject to a state or trade secret
RIV identification code RIV/00216224:14310/06:00025047
Organization unit Faculty of Science
Keywords in English Cartan geometry; parabolic geometry; symmetric space
Tags Cartan geometry, parabolic geometry, symmetric space
Tags International impact, Reviewed
Changed by Changed by: doc. Mgr. Lenka Zalabová, Ph.D., učo 13779. Changed: 28/11/2008 11:34.
Abstract
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.
Abstract (in Czech)
V článku se zabýváme symetriemi filtrovaných variet a detailně studujeme zejména jednagradované parabolické geometrie. Diskutujeme existenci symetrií na homogením modelu a uvedeme nějaká základní fakta o křivých modelech. Ukážeme, že existence symetrie v nějakém bodě nuluje torzi v tomto bodě. Obecná teorie parabolických geometrií pak ukazuje, že většina symetrických geometrií je lokálně plochá.
Links
GD201/05/H005, research and development projectName: Algebra a geometrie: propojení a trendy v současné matematice
Investor: Czech Science Foundation, Algebra and Geometry: the reunion and trends in current mathematics
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