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Currently displaying 1 – 4 of 4

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On completeness of left-invariant Lorentz metrics on solvable Lie groups.

Mohammed Guediri — 1996

Revista Matemática de la Universidad Complutense de Madrid

We study geodesic completeness for left-invariant Lorentz metrics on solvable Lie groups.

On the geodesic connectedness of simply connected Lorentz surfaces

Mohammed Guediri — 1997

Annales de la Faculté des sciences de Toulouse : Mathématiques

Erratum to “On the geodesic connectedness of simply connected Lorentz surfaces”

Mohammed Guediri — 2001

Annales de la Faculté des sciences de Toulouse : Mathématiques

Ricci-flat left-invariant Lorentzian metrics on 2-step nilpotent Lie groups

Mohammed Guediri; Mona Bin-Asfour — 2014

Archivum Mathematicum

The purpose of this paper is to investigate Ricci-flatness of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups. We first show that if $〈,〉$ is a Ricci-flat left-invariant Lorentzian metric on a 2-step nilpotent Lie group $N$ , then the restriction of $〈,〉$ to the center of the Lie algebra of $N$ is degenerate. We then characterize the 2-step nilpotent Lie groups which can be endowed with a Ricci-flat left-invariant Lorentzian metric, and we deduce from this that a Heisenberg Lie group $H_{2 n + 1}$ can be...

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