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ZALABOVÁ, Lenka. Symmetries of almost Grassmannian geometries. In Differential geometry and its applications. 1st ed. USA: World Scientific, 2008. p. 371-381, 10 pp. ISBN 978-981-279-060-6.
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Basic information
Original name Symmetries of almost Grassmannian geometries
Name in Czech Symetrie skorograssmannovských geometrií
Authors ZALABOVÁ, Lenka (203 Czech Republic, guarantor).
Edition 1. vyd. USA, Differential geometry and its applications, p. 371-381, 10 pp. 2008.
Publisher World Scientific
Other information
Original language English
Type of outcome Proceedings paper
Field of Study 10101 Pure mathematics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
RIV identification code RIV/00216224:14310/08:00025056
Organization unit Faculty of Science
ISBN 978-981-279-060-6
Keywords in English Cartan geometries; parabolic geometries; almost Grassmannian structures; almost quaternionic structures; symmetric spaces
Tags almost Grassmannian structures, almost quaternionic structures, Cartan geometries, parabolic geometries, symmetric spaces
Tags International impact, Reviewed
Changed by Changed by: doc. Mgr. Lenka Zalabová, Ph.D., učo 13779. Changed: 28/11/2008 11:52.
Abstract
We study symmetries of almost Grassmannian and almost quaternionic structures. We generalize the classical definition for locally symmetric spaces and we discuss the existence of symmetries on the homogeneous models. We proves the local flatness of the symmetric geometries for most cases of almost Grassmannian geometries. There are also some more interesting types of almost Grassmannian and almost quaternionic geometries, which can carry some symmetry in the point with nonzero curvature. We show, that there can be at most one symmetry in such point.
Abstract (in Czech)
Studujeme symetrie skorograssmannovských a skorokvaternionových geometrií. Zobecníme klasickou definici pro lokálně symetrické prostory a diskutujeme existenci symetrií na homogenním modelu. Ukážeme, že ve většině případů je symetrická geometrie lokálně plochá. Existují i zajímavější případy skorograssmannovských a skorokvaternionových geometrií, které mohou mít symetrii v bodě s nenulovou křivostí. Ukážeme, že v takovém případě může existovat nejvýše jedna symetrie.
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
Displayed: 9/12/2022 19:18