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 almost a...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2010
Hauptverfasser: Calvaruso, G., García-Río, E.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2010
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146096
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-146096
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups
spellingShingle Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups
Calvaruso, G.
García-Río, E.
title_short 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_sort algebraic properties of curvature operators in lorentzian manifolds with large isometry groups
author Calvaruso, G.
García-Río, E.
author_facet Calvaruso, G.
García-Río, E.
publishDate 2010
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/146096
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.
work_keys_str_mv AT calvarusog algebraicpropertiesofcurvatureoperatorsinlorentzianmanifoldswithlargeisometrygroups
AT garciarioe algebraicpropertiesofcurvatureoperatorsinlorentzianmanifoldswithlargeisometrygroups
first_indexed 2025-12-07T15:40:57Z
last_indexed 2025-12-07T15:40:57Z
_version_ 1850864626292490240