Holonomy of Einstein Lorentzian manifolds
Differential Geometry
2010-04-14 v3 High Energy Physics - Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0906.1327,
title = {Holonomy of Einstein Lorentzian manifolds},
author = {Anton S. Galaev},
journal= {arXiv preprint arXiv:0906.1327},
year = {2010}
}
Comments
Dedicated to to Mark Volfovich Losik on his 75th birthday. This version is an extended part of the previous version; another part of the previous version is extended and submitted as arXiv:1001.4441