Some applications of the Lorentzian holonomy algebras

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Authors

GALAEV Anton

Year of publication 2012
Type Article in Periodical
Magazine / Source Journal of Geometry and Symmetry in Physics
MU Faculty or unit

Faculty of Science

Citation
Web http://www.bio21.bas.bg/jgsp/jgsp_files/vol26/volume26cont.html
Field General mathematics
Keywords Lorentzian manifold; holonomy algebra; recurrent Weyl tensor
Description 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.
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