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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)
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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
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\by Giovanni Calvaruso, Eduardo Garc{\'\i}a-R{\'\i}o
\paper Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups
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\vol 6
\papernumber 005
\totalpages 8
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Symmetry, Integrability and Geometry: Methods and Applications
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