Journal of Geometry and Symmetry in Physics

Some Applications of the Lorentzian Holonomy Algebras

Anton Galaev

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

Dates
First available in Project Euclid: 25 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.jgsp/1495699224

Digital Object Identifier
doi:10.7546/jgsp-26-2012-13-31

Mathematical Reviews number (MathSciNet)
MR2986250

Zentralblatt MATH identifier
1261.53048

Citation

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. https://projecteuclid.org/euclid.jgsp/1495699224


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