Alignment classification of tensors on Lorentzian manifolds of arbitrary dimension is summarized. This classification scheme is then applied to the case of the Weyl tensor and it is shown that in four dimensions it is equivalent to the well known Petrov classification. The approaches using Bel-Debever criteria and principal null directions of the superenergy tensor are also discussed.
@article{702908,
title = {Algebraic classification of the Weyl tensor},
booktitle = {Applications of Mathematics 2012},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2012},
pages = {224-235},
mrnumber = {MR3204414},
zbl = {1313.53081},
url = {http://dml.mathdoc.fr/item/702908}
}
Pravdová, Alena. Algebraic classification of the Weyl tensor, dans Applications of Mathematics 2012, GDML_Books, (2012), pp. 224-235. http://gdmltest.u-ga.fr/item/702908/