Holonomy of Einstein Lorentzian manifolds

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Authors

GALAEV Anton

Year of publication 2010
Type Article in Periodical
Magazine / Source Classical and Quantum Gravity
MU Faculty or unit

Faculty of Science

Citation
Web http://iopscience.iop.org/0264-9381/27/7/075008/
Field General mathematics
Keywords Holonomy algebra - Einstein and Ricci-flat Lorentzian manifolds
Description The classification of all possible holonomy algebras of Einstein and vacuum Einstein Lorentzian manifolds is obtained. It is shown that each such algebra appears as the holonomy algebra of an Einstein (resp. vacuum Einstein) Lorentzian manifold; the direct constructions are given. Also the holonomy algebras of totally Ricci-isotropic Lorentzian manifolds are classified. The classification of the holonomy algebras of Lorentzian manifolds is reviewed and a complete description of the spaces of curvature tensors for these holonomies is given.
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