Local Generalized Symmetries and Locally Symmetric Parabolic Geometries

Local Generalized Symmetries and Locally Symmetric Parabolic Geometries

We investigate (local) automorphisms of parabolic geometries that generalize geodesic symmetries. We show that many types of parabolic geometries admit at most one generalized geodesic symmetry at a point with non-zero harmonic curvature. Moreover, we show that if there is exactly one symmetry at ea...

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Date:2017
Main Authors: Gregorovič, J., Zalabová, L.
Format: Article
Language:English
Published: Інститут математики НАН України 2017
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/148627
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Local Generalized Symmetries and Locally Symmetric Parabolic Geometries / J. Gregorovič, L. Zalabová // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 25 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1486272019-02-19T01:30:02Z Local Generalized Symmetries and Locally Symmetric Parabolic Geometries Gregorovič, J. Zalabová, L. We investigate (local) automorphisms of parabolic geometries that generalize geodesic symmetries. We show that many types of parabolic geometries admit at most one generalized geodesic symmetry at a point with non-zero harmonic curvature. Moreover, we show that if there is exactly one symmetry at each point, then the parabolic geometry is a generalization of an affine (locally) symmetric space. 2017 Article Local Generalized Symmetries and Locally Symmetric Parabolic Geometries / J. Gregorovič, L. Zalabová // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 25 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53C10; 53C22; 53C15; 53C05; 53B15; 53A55 DOI:10.3842/SIGMA.2017.032 http://dspace.nbuv.gov.ua/handle/123456789/148627 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description We investigate (local) automorphisms of parabolic geometries that generalize geodesic symmetries. We show that many types of parabolic geometries admit at most one generalized geodesic symmetry at a point with non-zero harmonic curvature. Moreover, we show that if there is exactly one symmetry at each point, then the parabolic geometry is a generalization of an affine (locally) symmetric space.
format Article
author Gregorovič, J.
Zalabová, L.
spellingShingle Gregorovič, J.
Zalabová, L.
Local Generalized Symmetries and Locally Symmetric Parabolic Geometries
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Gregorovič, J.
Zalabová, L.
author_sort Gregorovič, J.
title Local Generalized Symmetries and Locally Symmetric Parabolic Geometries
title_short Local Generalized Symmetries and Locally Symmetric Parabolic Geometries
title_full Local Generalized Symmetries and Locally Symmetric Parabolic Geometries
title_fullStr Local Generalized Symmetries and Locally Symmetric Parabolic Geometries
title_full_unstemmed Local Generalized Symmetries and Locally Symmetric Parabolic Geometries
title_sort local generalized symmetries and locally symmetric parabolic geometries
publisher Інститут математики НАН України
publishDate 2017
url http://dspace.nbuv.gov.ua/handle/123456789/148627
citation_txt Local Generalized Symmetries and Locally Symmetric Parabolic Geometries / J. Gregorovič, L. Zalabová // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 25 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT gregorovicj localgeneralizedsymmetriesandlocallysymmetricparabolicgeometries
AT zalaboval localgeneralizedsymmetriesandlocallysymmetricparabolicgeometries
first_indexed 2025-07-12T19:48:59Z
last_indexed 2025-07-12T19:48:59Z
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