Journal of Geometry and Symmetry in Physics

Some Applications of the Lorentzian Holonomy Algebras

Anton Galaev

Full-text: Open access


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 and the classification of two-symmetric Lorentzian manifolds is explained. Then the conformally recurrent Lorentzian manifolds are classified and the recurrent symmetric bilinear forms on these manifolds are described.

Article information

J. Geom. Symmetry Phys., Volume 26 (2012), 13-31.

First available in Project Euclid: 25 May 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Galaev, Anton. Some Applications of the Lorentzian Holonomy Algebras. J. Geom. Symmetry Phys. 26 (2012), 13--31. doi:10.7546/jgsp-26-2012-13-31.

Export citation