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Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups
Інший ID:
2010 Mathematics Subject Classification: 53C50; 53C20
Посилання:
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.
Підтримка:
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.
Дата:
2010
Переглядів:
634
Завантажень:
265
Анотація:
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.
