Proceedings of the International Conference on Geometry, Integrability and Quantization

Some Applications of the Lorentzian Holonomy Algebras

Anton Galaev

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 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

Source
Proceedings of the Thirteenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Andrei Ludu and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2012), 132-149

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815522

Digital Object Identifier
doi:10.7546/giq-13-2012-132-149

Mathematical Reviews number (MathSciNet)
MR3087968

Zentralblatt MATH identifier
1382.53016

Citation

Galaev, Anton. Some Applications of the Lorentzian Holonomy Algebras. Proceedings of the Thirteenth International Conference on Geometry, Integrability and Quantization, 132--149, Avangard Prima, Sofia, Bulgaria, 2012. doi:10.7546/giq-13-2012-132-149. https://projecteuclid.org/euclid.pgiq/1436815522


Export citation