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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2010, том 6, 005, 8 стр. (Mi sigma462)

Эта публикация цитируется в 3 статьях

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

Аннотация: 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.

Ключевые слова: 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.

MSC: 53C50; 53C20

Поступила: 1 октября 2009 г.; в окончательном варианте 7 января 2010 г.; опубликована 12 января 2010 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2010.005



Реферативные базы данных:
ArXiv: 1001.1994


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