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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
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
Citation:
Giovanni Calvaruso, Eduardo García-Río, “Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups”, SIGMA, 6 (2010), 005, 8 pp.
Linking options:
https://www.mathnet.ru/eng/sigma462 https://www.mathnet.ru/eng/sigma/v6/p5
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