On the Einstein equation on Lorentzian manifolds with parallel distributions of isotropic lines

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Authors	GALAEV Anton
Year of publication	2011
Type	Article in Periodical
Magazine / Source	Sci. Proc. Kazan Univ.
MU Faculty or unit	Faculty of Science
Citation
Web	http://mi.mathnet.ru/uzku1064
Field	General mathematics
Keywords	Lorentzian manifold; Einstein equation; Walker metric; holonomy algebra
Description	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.
Related projects:	Mathematical structures and their physical applications Holonomy of Riemannian supermanifolds and related geometric structures