Metrics that realize all Lorentzian holonomy algebras
Anton S. Galaev
Abstract
All candidates to the weakly-irreducible not irreducible holonomy algebras of Lorentzian manifolds are known. In the present paper metrics that realize all these candidates as holonomy algebras are given. This completes the classification of the Lorentzian holonomy algebras. Also new examples of metrics with the holonomy algebras g27⊂(1,8) and (7)8⊂(1,9) are constructed.
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