On Lie groups that admit left-invariant Lorentz metrics of constant sectional curvature
Let G be a Lie group which admits a left-invariant Riemannian metric of constant negative sectional curvature. The main theorem in this paper states that: i) G admits a left-invariant Lorentz metric of constant positive sectional curvature, ii) G admits a left-invariant Lorentz metric of constant negative, or zero, sectional curvature if and only if its Lie algebra contains a one-dimensional ideal. Combining this with a previous result of E. Heintze, the author proves that such even- dimensional groups G admit left-invariant Lorentz metrics with constant sectional curvature of any possible sign, whereas this may be wrong for odd-dimensional groups.
scientific article; zbMATH DE number 4113455