On completeness of left-invariant Lorentz metrics on solvable Lie groups.
We study geodesic completeness for left-invariant Lorentz metrics on solvable Lie groups.
On the geodesic connectedness of simply connected Lorentz surfaces
Erratum to “On the geodesic connectedness of simply connected Lorentz surfaces”
Ricci-flat left-invariant Lorentzian metrics on 2-step nilpotent Lie groups
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 , then the restriction of to the center of the Lie algebra of 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 can be...
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