Investigation of conformally killing vector fields on 5-dimensional 2-symmetric lorentzian manifolds

Conformally Killing fields play an important role in the theory of Ricci solitons and also generate an important class of locally conformally homogeneous (pseudo) Riemannian manifolds. In the Riemannian case, V. V. Slavsky and E.D. Rodionov proved that such spaces are either conformally flat or conformally equivalent to locally homogeneous Riemannian manifolds. In the pseudo-Riemannian case, the question of their structure remains open. Pseudo-Riemannian symmetric spaces of order k, where k 2, play an important role in research in pseudo-Riemannian geometry. Currently, they have been investigated in cases k=2,3 by D.V. Alekseevsky, A.S. Galaev and others. For arbitrary k, non-trivial examples of such spaces are known: generalized Kachen - Wallach manifolds. In the case of small dimensions, these spaces and Killing vector fields on them were studied by D.N. Oskorbin, E.D. Rodionov, and I.V. Ernst with the helpof systems of computer mathematics. In this paper, using the Sagemath SCM, we investigate conformally Killing vector fields on five-dimensional indecomposable 2- symmetric Lorentzian manifolds, and construct an algorithm for their computation.

On Golden Lorentzian Manifolds Equipped with Generalized Symmetric Metric Connection

This research deals with the generalized symmetric metric U-connection defined on golden Lorentzian manifolds. We also derive sharp geometric inequalities that involve generalized normalized δ-Casorati curvatures for submanifolds of golden Lorentzian manifolds equipped with generalized symmetric metric U-connection.

Construction of Initial Data Sets for Lorentzian Manifolds with Lightlike Parallel Spinors

Lorentzian manifolds with parallel spinors are important objects of study in several branches of geometry, analysis and mathematical physics. Their Cauchy problem has recently been discussed by Baum, Leistner and Lischewski, who proved that the problem locally has a unique solution up to diffeomorphisms, provided that the intial data given on a space-like hypersurface satisfy some constraint equations. In this article we provide a method to solve these constraint equations. In particular, any curve (resp. closed curve) in the moduli space of Riemannian metrics on M with a parallel spinor gives rise to a solution of the constraint equations on $$M\times (a,b)$$ M × ( a , b ) (resp. $$M\times S^1$$ M × S 1 ).

Gravitating Meron-like topological solitons in massive Yang–Mills theory and the Einstein–Skyrme model

We show that Merons in D-dimensional Einstein–Massive–Yang–Mills theory can be mapped to solutions of the Einstein–Skyrme model. The identification of the solutions relies on the fact that, when considering the Meron ansatz for the gauge connection $$A=\lambda U^{-1}dU$$ A = λ U - 1 d U , the massive Yang–Mills equations reduce to the Skyrme equations for the corresponding group element U. In the same way, the energy–momentum tensors of both theories can be identified and therefore lead to the same Einstein equations. Subsequently, we focus on the SU(2) case and show that introducing a mass for the Yang–Mills field restricts Merons to live on geometries given by the direct product of $$S^3$$ S 3 (or $$S^2$$ S 2 ) and Lorentzian manifolds with constant Ricci scalar. We construct explicit examples for $$D=4$$ D = 4 and $$D=5$$ D = 5 . Finally, we comment on possible generalisations.

A classification of Roter type spacetimes

In this paper, an algebraic classification of the Roter type spacetimes is given. It follows that the Roter type curvature condition is essentially equivalent with the pseudosymmetry condition on 4-dimensional Lorentzian manifolds.

Compact null hypersurfaces in Lorentzian manifolds

We show how the topological and geometric properties of the family of null hypersurfaces in a Lorentzian manifold are related with the properties of the ambient manifold itself. In particular, we focus in how the presence of global symmetries and curvature conditions restrict the existence of compact null hypersurfaces. We use these results to show the influence on the existence of compact totally umbilic null hypersurfaceswhich are not totally geodesic. Finally we describe the restrictions that they impose in causality theory.