In this work, we firstly introduce notions of principal directed curves and donor which are associated a Frenet curve in the dual Lorentzian space D 3 1 D13 . We give some relations between curvature torsion curve. show that general helix is plane obtain equation by using position vector Then circle $\mathbb{D}^{2}$ or hyperbola $\mathbb{D}_{1}^{2}$ slant $\mathbb{D}_{1}^{3}$ helix, respectivel...

The structure of the general, inhomogeneous solution of (bosonic) Einstein-matter systems in the vicinity of a cosmological singularity is considered. We review the proof (based on ideas of BelinskiiKhalatnikov-Lifshitz and technically simplified by the use of the ArnowittDeser-Misner Hamiltonian formalism) that the asymptotic behaviour, as one approaches the singularity, of the general solutio...

Abstract. We present in this paper a C-metric on an open neighbourhood of the origin in R5. The metric is of Lorentzian signature (1, 4) and admits a solution to the twistor equation for spinors with a unique isolated zero at the origin. The metric is not conformally flat in any neighbourhood of the origin. The construction is based on the Eguchi-Hanson metric with parallel spinors on Riemannia...

In this article, we try to understand the mechanisms of the non properness of the action of the group of diffeomorphisms on the space of Lorentzian metrics of a compact manifold. We give a first result that describes the dynamical behavior of the sequences of diffeomorphisms involved which entails the existence of metrics that admit an isotropic geodesic foliation of codimension 1. On the 2-tor...

In this article, we try to understand the mechanisms of the non properness of the action of the group of diffeomorphisms on the space of Lorentzian metrics of a compact manifold. We give a first result that describes the dynamical behavior of the sequences of diffeomorphisms involved which entails the existence of metrics that admit an isotropic geodesic foliation of codimension 1. On the 2-tor...