Geodesic
On the Einstein equation on Lorentzian manifolds with parallel distributions of isotropic lines
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 165-174

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Some recent results about Einstein Lorentzian manifolds that admit parallel distributions of isotropic lines are reviewed. We find all holonomy algebras of such manifolds and describe special coordinates that allow us to simplify the Einstein equation. Examples in dimension 4 are considered.
Keywords: Lorentzian manifold, Einstein equation, Walker metric, holonomy algebra, recurrent light-like vector field, Petrov classification. 
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     author = {A. S. Galaev},
     title = {On the {Einstein} equation on {Lorentzian} manifolds with parallel distributions of isotropic lines},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {165--174},
     publisher = {mathdoc},
     volume = {153},
     number = {3},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a14/}
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A. S. Galaev. On the Einstein equation on Lorentzian manifolds with parallel distributions of isotropic lines. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 165-174. http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a14/