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.
Related projects:	Mathematical structures and their physical applications Holonomy of Riemannian supermanifolds and related geometric structures