Four-dimensional Lorentzian Lie groups (Q385747)
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scientific article; zbMATH DE number 6237572
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Four-dimensional Lorentzian Lie groups |
scientific article; zbMATH DE number 6237572 |
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Four-dimensional Lorentzian Lie groups (English)
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11 December 2013
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Lie group
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left-invariant metric
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Einsteinian metric
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Ricci soliton
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The geometric classifications of some classes of four-dimensional simply connected Lie groups with invariant Lorenzian metrics are given.NEWLINENEWLINEUp to an isomorphism of Lie groups the classification of four-dimensional simply connected Lie groups with invariant Lorenzian metrics is well known. NEWLINENEWLINENEWLINEIn this paper the authors give explicit classification (up to isometry) of the Einsteinian Lorenzian four-dimensional simply connected Lie groups and the four-dimensional simply connected Lie groups with invariant Ricci-parallel (not Einsteinian) Lorenzian metrics. Then examples of Ricci solitons are listed.
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