  We consider Lie groups equipped with a left-invariant cyclic Lorentzian
metric. As in the Riemannian case, in terms of homogeneous structures, such
metrics can be considered as different as possible from bi-invariant metrics.
We show that several results concerning cyclic Riemannian metrics do not extend
to their Lorentzian analogues, and obtain a full classification of three- and
four-dimensional cyclic Lorentzian metrics.

Differential Geometry