Holonomy groups of Lorentzian manifolds
ثبت نشده
چکیده
In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian metrics with all possible connected holonomy groups is obtained. As the applications, the Einstein equation, Lorentzian manifolds with parallel and recurrent spinor fields, conformally flat Walker metrics and the classification of 2-symmetric Lorentzian manifolds are considered. Bibliography: 123 titles.
منابع مشابه
The conformal analog of Calabi-Yau manifolds
This survey intends to introduce the reader to holonomy theory of Cartan connections. Special attention is given to the normal conformal Cartan connection, uniquely defined for a class of conformally equivalent metrics, and to its holonomy group the ’conformal holonomy group’. We explain the relation between conformal holonomy group and existence of Einstein metrics in the conformal class as we...
متن کاملScreen bundles of Lorentzian manifolds and some generalisations of pp-waves
A pp-wave is a Lorentzian manifold with a parallel light-like vector field satisfying a certain curvature condition. We introduce generalisations of pp-waves, on one hand by allowing the vector field to be recurrent and on the other hand by weakening the curvature condition. These generalisations are related to the screen holonomy of the Lorentzian manifold. While pp-waves have a trivial screen...
متن کاملTowards a classification of Lorentzian holonomy groups. Part II: Semisimple, non-simple weak-Berger algebras
The holonomy group of an (n+2)–dimensional simply-connected, indecomposable but non-irreducible Lorentzian manifold (M,h) is contained in the parabolic group (R × SO(n)) ⋉ R. The main ingredient of such a holonomy group is the SO(n)–projection G := prSO(n)(Holp(M,h)) and one may ask whether it has to be a Riemannian holonomy group. In this paper we show that this is always the case, completing ...
متن کاملConformal holonomy of C-spaces, Ricci-flat, and Lorentzian manifolds
The main result of this paper is that a Lorentzian manifold is locally conformally equivalent to a manifold with recurrent lightlike vector field and totally isotropic Ricci tensor if and only if its conformal tractor holonomy admits a 2-dimensional totally isotropic invariant subspace. Furthermore, for semi-Riemannian manifolds of arbitrary signature we prove that the conformal holonomy algebr...
متن کاملOn $(epsilon)$ - Lorentzian para-Sasakian Manifolds
The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.
متن کامل