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: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| 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| _version_ | 1862602266918256640 |
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| author | Gregorovič, J. Zalabová, L. |
| author_facet | Gregorovič, J. Zalabová, L. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-28T02:25:30Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148627 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-28T02:25:30Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | Local Generalized Symmetries and Locally Symmetric Parabolic Geometries Gregorovič, J. Zalabová, L. |
| title | 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_short | Local Generalized Symmetries and Locally Symmetric Parabolic Geometries |
| title_sort | local generalized symmetries and locally symmetric parabolic geometries |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148627 |
| work_keys_str_mv | AT gregorovicj localgeneralizedsymmetriesandlocallysymmetricparabolicgeometries AT zalaboval localgeneralizedsymmetriesandlocallysymmetricparabolicgeometries |