Some applications of the Lorentzian holonomy algebras

TL;DR

This paper applies Lorentzian holonomy algebra classification to address problems like recurrent curvature, two-symmetry, and conformal recurrence in Lorentzian manifolds, providing new proofs and classifications.

Contribution

It offers new proofs and classifications for recurrent curvature, two-symmetric, and conformally recurrent Lorentzian manifolds using holonomy algebra methods.

Findings

New proof of Lorentzian manifolds with recurrent curvature tensor

Classification of two-symmetric Lorentzian manifolds

Classification of conformally recurrent Lorentzian manifolds

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.