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

A. S. Galaev

Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic

Abstract: 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.

UDC: 514.83

Received: 06.12.2010

Language: English