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.

References in corpus (4)

• Screen bundles of Lorentzian manifolds and some generalisations of pp-waves
• Two-symmetric Lorentzian manifolds
• On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines
• One component of the curvature tensor of a Lorentzian manifold

Cited by in corpus (3)

• On conformally recurrent manifolds of dimension greater than 4
• Homogeneity of Lorentzian three-manifolds with recurrent curvature
• Locally Conformally Flat Lorentzian Gradient Ricci Solitons