17,954 research outputs found
Examples of Einstein spacetimes with recurrent null vector fields
The Einstein Equation on 4-dimensional Lorentzian manifolds admitting
recurrent null vector fields is discussed. Several examples of a special form
are constructed. The holonomy algebras, Petrov types and the Lie algebras of
Killing vector fields of the obtained metrics are found.Comment: 7 pages, the final versio
About the classification of the holonomy algebras of Lorentzian manifolds
The classification of the holonomy algebras of Lorentzian manifolds can be
reduced to the classification of irreducible subalgebras
that are spanned by the images of linear
maps from to satisfying an identity similar to
the Bianchi one. T. Leistner found all such subalgebras and it turned out that
the obtained list coincides with the list of irreducible holonomy algebras of
Riemannian manifolds. The natural problem is to give a simple direct proof to
this fact. We give such proof for the case of semisimple not simple Lie
algebras .Comment: 9 pages, the final versio
Isometry groups of Lobachevskian spaces, similarity transformation groups of Euclidean spaces and Lorentzian holonomy groups
Weakly-irreducible not irreducible subalgebras of \so(1,n+1) were
classified by L. Berard Bergery and A. Ikemakhen. In the present paper a
geometrical proof of this result is given. Transitively acting isometry groups
of Lobachevskian spaces and transitively acting similarity transformation
groups of Euclidean spaces are classified.Comment: 12 page
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