ZALABOVÁ, Lenka. Symmetries of parabolic geometries. Differential Geometry and its Applications. Amsterdam: Elsevier Science, 2009, vol. 27, No 5, p. 605-622. ISSN 0926-2245.
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Basic information
Original name Symmetries of parabolic geometries
Name in Czech Symetrie parabolických geometrií
Authors ZALABOVÁ, Lenka (203 Czech Republic, guarantor).
Edition Differential Geometry and its Applications, Amsterdam, Elsevier Science, 2009, 0926-2245.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher Netherlands
Confidentiality degree is not subject to a state or trade secret
Impact factor Impact factor: 0.669
RIV identification code RIV/00216224:14310/09:00029992
Organization unit Faculty of Science
UT WoS 000270635200003
Keywords in English Cartan geometries; Parabolic geometries; |1|-graded geometries; Weyl structures; Symmetric spaces
Tags International impact, Reviewed
Changed by Changed by: doc. Mgr. Vojtěch Žádník, Ph.D., učo 8753. Changed: 25/3/2010 15:28.
Abstract
We generalize the concept of affine locally symmetric spaces for parabolic geometries. We discuss mainly |1|-graded geometries and we show some restrictions on their curvature coming from the existence of symmetries. We use the theory of Weyl structures to discuss more interesting |1|-graded geometries which can carry a symmetry in a point with nonzero curvature. More concretely, we discuss the number of different symmetries which can exist at the point with nonzero curvature.
Abstract (in Czech)
Zobecňujeme koncept afinních symetrických prostorů na parabolické geometrie. Diskutujeme zejména jednagradované geometrie a ukazujeme omezení na jejich křivost, která jsou způsobena existencí symetrií. Využíváme teorii Weylových struktur ke studiu zajímavějších příkladů geometrií, které mohou nést symetrie v bodech s nenulovou křivostí. Diskutujeme zejména počet symetrií, které mohou existovat v bodech s nenulovou křivostí.
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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