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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2017
Main Authors: Gregorovič, J., Zalabová, L.
Format: Article
Language:English
Published: Інститут математики НАН України 2017
Online Access:https://nasplib.isofts.kiev.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
id nasplib_isofts_kiev_ua-123456789-148627
record_format dspace
spelling Gregorovič, J.
Zalabová, L.
2019-02-18T16:45:23Z
2019-02-18T16:45:23Z
2017
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
https://nasplib.isofts.kiev.ua/handle/123456789/148627
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.
JG supported by the Grant agency of the Czech Republic under the grant GBP201/12/G028. The authors would like to thank the anonymous referees for their valuable comments which helped to improve the manuscript.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Local Generalized Symmetries and Locally Symmetric Parabolic Geometries
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Local Generalized Symmetries and Locally Symmetric Parabolic Geometries
spellingShingle Local Generalized Symmetries and Locally Symmetric Parabolic Geometries
Gregorovič, J.
Zalabová, L.
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
author Gregorovič, J.
Zalabová, L.
author_facet Gregorovič, J.
Zalabová, L.
publishDate 2017
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.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.
work_keys_str_mv AT gregorovicj localgeneralizedsymmetriesandlocallysymmetricparabolicgeometries
AT zalaboval localgeneralizedsymmetriesandlocallysymmetricparabolicgeometries
first_indexed 2025-11-28T02:25:30Z
last_indexed 2025-11-28T02:25:30Z
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