Some applications of the Lorentzian holonomy algebras

Abstract

It is shown how one can apply the classification of the holonomy algebras of Lorentzian manifolds to solve some problems. In particular, a new proof to the classification of Lorentzian manifolds with recurrent curvature tensor is given; the classification of two-symmetric Lorentzian manifolds is explained; conformally recurrent Lorentzian manifolds are classified; recurrent symmetric bilinear forms on Lorentzian manifolds are described.