Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 005, 8 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.005
(Mi sigma462)
 

This article is cited in 3 scientific papers (total in 3 papers)

Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups

Giovanni Calvarusoa, Eduardo García-Ríob

a Dipartimento di Matematica "E. De Giorgi", Università del Salento, Lecce, Italy
b Faculty of Mathematics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
Full-text PDF (206 kB) Citations (3)
References:
Abstract: Together with spaces of constant sectional curvature and products of a real line with a manifold of constant curvature, the socalled Egorov spaces and $\varepsilon$-spaces exhaust the class of $n$-dimensional Lorentzian manifolds admitting a group of isometries of dimension at least $\frac12 n(n-1)+1$, for almost all values of $n$ [Patrangenaru V., Geom. Dedicata 102 (2003), 25–33]. We shall prove that the curvature tensor of these spaces satisfy several interesting algebraic properties. In particular, we will show that Egorov spaces are Ivanov–Petrova manifolds, curvature-Ricci commuting (indeed, semi-symmetric) and $\mathcal P$-spaces, and that $\varepsilon$-spaces are Ivanov–Petrova and curvature-curvature commuting manifolds.
Keywords: Lorentzian manifolds; skew-symmetric curvature operator; Jacobi, Szabó and skew-symmetric curvature operators; commuting curvature operators; IP manifolds; $\mathcal C$-spaces and $\mathcal P$-spaces.
Received: October 1, 2009; in final form January 7, 2010; Published online January 12, 2010
Bibliographic databases:
Document Type: Article
MSC: 53C50; 53C20
Language: English
Citation: Giovanni Calvaruso, Eduardo García-Río, “Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups”, SIGMA, 6 (2010), 005, 8 pp.
Citation in format AMSBIB
\Bibitem{CalGar10}
\by Giovanni Calvaruso, Eduardo Garc{\'\i}a-R{\'\i}o
\paper Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups
\jour SIGMA
\yr 2010
\vol 6
\papernumber 005
\totalpages 8
\mathnet{http://mi.mathnet.ru/sigma462}
\crossref{https://doi.org/10.3842/SIGMA.2010.005}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2593377}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000273562500005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84880701636}
Linking options:
  • https://www.mathnet.ru/eng/sigma462
  • https://www.mathnet.ru/eng/sigma/v6/p5
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:552
    Full-text PDF :65
    References:49
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024