Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups
Together with spaces of constant sectional curvature and products of a real line
 with a manifold of constant curvature, the socalled Egorov spaces and ε-spaces exhaust the class of n-dimensional Lorentzian manifolds admitting a group of isometries of dimension at least 0.5n(n − 1) + 1, for...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2010 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2010
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146096 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups / E. García-Río // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862678626373206016 |
|---|---|
| author | Calvaruso, G. García-Río, E. |
| author_facet | Calvaruso, G. García-Río, E. |
| citation_txt | Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups / E. García-Río // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Together with spaces of constant sectional curvature and products of a real line
with a manifold of constant curvature, the socalled Egorov spaces and ε-spaces exhaust the class of n-dimensional Lorentzian manifolds admitting a group of isometries of dimension at least 0.5n(n − 1) + 1, for almost all values of n [Patrangenaru V., Geom. Dedicata 102 (2003), 25–33]. We shall prove that the curvature tensor of these spaces satisfi several interesting algebraic properties. In particular, we will show that Egorov spaces are Ivanov–Petrova manifolds, curvature-Ricci commuting (indeed, semi-symmetric) and P-spaces, and that ε-spaces are Ivanov–Petrova and curvature-curvature commuting manifolds.
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| first_indexed | 2025-12-07T15:40:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146096 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:40:57Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Calvaruso, G. García-Río, E. 2019-02-07T12:50:53Z 2019-02-07T12:50:53Z 2010 Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups / E. García-Río // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53C50; 53C20 https://nasplib.isofts.kiev.ua/handle/123456789/146096 Together with spaces of constant sectional curvature and products of a real line
 with a manifold of constant curvature, the socalled Egorov spaces and ε-spaces exhaust the class of n-dimensional Lorentzian manifolds admitting a group of isometries of dimension at least 0.5n(n − 1) + 1, for almost all values of n [Patrangenaru V., Geom. Dedicata 102 (2003), 25–33]. We shall prove that the curvature tensor of these spaces satisfi several interesting algebraic properties. In particular, we will show that Egorov spaces are Ivanov–Petrova manifolds, curvature-Ricci commuting (indeed, semi-symmetric) and P-spaces, and that ε-spaces are Ivanov–Petrova and curvature-curvature commuting manifolds. First author supported by funds of MIUR (PRIN 2007) and the University of Salento. Second
 author supported by projects MTM2009-07756 and INCITE09 207 151 PR (Spain). Finally the
 authors would like to express their thanks to the Referees of this paper for pointing out some
 mistakes in the original manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups Article published earlier |
| spellingShingle | Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups Calvaruso, G. García-Río, E. |
| title | Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups |
| title_full | Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups |
| title_fullStr | Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups |
| title_full_unstemmed | Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups |
| title_short | Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups |
| title_sort | algebraic properties of curvature operators in lorentzian manifolds with large isometry groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146096 |
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