Dynamical properties of the space of Lorentzian metrics . Pierre Mounoud

Dynamical properties of the space of Lorentzian metrics

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...

On Lorentzian two-Symmetric Manifolds of Dimension-fou‎r

‎We study curvature properties of four-dimensional Lorentzian manifolds with two-symmetry property‎. ‎We then consider Einstein-like metrics‎, ‎Ricci solitons and homogeneity over these spaces‎‎.

Spacelike hypersurfaces in Riemannian or Lorentzian space forms satisfying L_k(x)=Ax+b

We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k

Some geometrical properties of the oscillator group

‎We consider the oscillator group equipped with‎ ‎a biinvariant Lorentzian metric‎. ‎Some geometrical properties of this space and the harmonicity properties of left-invariant vector fields on this space are determined‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional‎ ‎restricted to vector fields‎. ‎Left-invariant vector fields defining harmonic maps are...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form