Holonomy of Einstein Lorentzian manifoldsDedicated to Mark Volfovich Losik on his 75th birthday

Anton S Galaev (1)

1 SCI / MUNI - Faculty of Science [Brno]

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.

Mots clés: Physical Sciences

Anton S Galaev. Holonomy of Einstein Lorentzian manifoldsDedicated to Mark Volfovich Losik on his 75th birthday. Classical and Quantum Gravity, 2010, 27 (7), pp.75008. ⟨10.1088/0264-9381/27/7/075008⟩. ⟨hal-00583900⟩