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A classification of left-invariant Lorentzian metrics on some nilpotent Lie groups. (English) Zbl 1517.53057

The authors classify left-invariant Lorentzian metrics on the direct product of the 3-dimensional Heisenberg group and the Euclidean space. They prove that, up to scaling and automorphisms, there exist exactly six such metrics, one of them is flat and the others are Ricci solitons but not Einstein.

MSC:

53C30 Differential geometry of homogeneous manifolds
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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References:

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