Compact flat spacetimes

Guediri, Mohammed

doi:10.1016/j.difgeo.2004.05.003

Cited by 6 publications

(6 citation statements)

References 17 publications

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“…In [2], Aubert and Medina showed that nilpotent flat Lorentzian Lie algebras are obtained by the double extension process from Riemannian abelian Lie algebras. In [4], Guediri studied Lie groups which may act isometrically and simply transitively on Minkowski space and get a precise description of nilpotent flat Lorentzian Lie groups. In [1], the authors showed that flat Lorentzian Lie algebras with degenerate center can be obtained by the double extension process from flat Riemannian Lie algebras.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Flat Nonunimodular Lorentzian Lie Algebras

Boucetta

Lebzioui

2016

Communications in Algebra

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A flat Lorentzian Lie algebra is a left symmetric algebra endowed with a symmetric bilinear form of signature − + + such that left multiplications are skewsymmetric. In geometrical terms, a flat Lorentzian Lie algebra is the Lie algebra of a Lie group with a left-invariant Lorentzian metric with vanishing curvature. In this article, we show that any flat nonunimodular Lorentzian Lie algebras can be obtained as a double extension of flat Riemannian Lie algebras. As an application, we give all flat nonunimodular Lorentzian Lie algebras up to dimension 4.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Flat Nonunimodular Lorentzian Lie Algebras

Boucetta

Lebzioui

2016

Communications in Algebra

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“…(See [40,50] for an exposition.) For example, a classification theory of compact flat Lorentzian manifolds is developed in [6,39,48,49,52].…”

Section: Structure Theory Of Compact Flat Pseudo-riemannian Manifoldsmentioning

confidence: 99%

Prehomogeneous affine representations and flat pseudo-Riemannian manifolds

Baues

2010

Handbook of Pseudo-Riemannian Geometry and Supersymmetry

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The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several aspects of this correspondence. At the heart of our presentation is a development of the theory of characteristic classes and characters of prehomogeneous affine representations. We give applications concerning flat affine, as well as Pseudo-Riemannian and symplectic affine flat manifolds.

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“…Notice that since U is normal in A (G) , we have A (G) ⊆ N (U ) by definition of N (U ) . Since is cocompact, we deduce from Theorem 1.2.1 of [7] that it suffices to consider the particular case where G does not contain elliptic automorphisms, that is, R is purely a hyperbolic one-parameter subgroup (for details, see [19]). On the other hand, as we can check easily, L (U ) preserves a null vector (compare [11], p. 388).…”

Section: Closed Timelike Geodesics In Compact Flat Spacetimesmentioning

confidence: 99%

“…This will contain the results in [1] for n = 3 and results in [11] for n = 4 as special cases. The substantial material for such a classification is contained in the proof of Theorem 4.1, and this will be the aim of a further publication [19].…”

Section: Remarkmentioning

confidence: 99%

On the existence of closed timelike geodesics in compact spacetimes. II

Guediri¹

2003

Math. Z.

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The purpose of this paper is on the one hand to extend and generalize, in terms of Clifford translations, some results in a previous paper (Math. Z. 239 (2002), 277-291) concerning the existence of closed timelike geodesics in compact spacetimes, and on the other hand to prove that a compact flat spacetime (M, g) contains a closed timelike geodesic if and only if the fundamental group π 1 (M) contains a non-trivial timelike translation. (2000): 53C50, 53C22. Mathematics Subject Classification

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Compact flat spacetimes

Cited by 6 publications

References 17 publications

Flat Nonunimodular Lorentzian Lie Algebras

Flat Nonunimodular Lorentzian Lie Algebras

Prehomogeneous affine representations and flat pseudo-Riemannian manifolds

On the existence of closed timelike geodesics in compact spacetimes. II

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