In this paper, we introduce some inequalities for screen homothetic half lightlike submanifolds of a real space form constant sectional curvature , endowed with semi-symmetric metric connection. Using these inequalities, derive characterizations such submanifolds. Finally, Chen-Ricci are calculated. Morever, the equality cases considered and get results.

The problem of geodesic connectedness in semi-Riemannian manifolds (i.e. the question whether each two points of the manifold can be joined by a geodesic) has been widely studied from very different viewpoints. Our purpose is to review these semi-Riemannian techniques, and possible extensions. In the Riemannian case, it is natural to state this problem on (incomplete) manifolds with (possibly n...

We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed into one of the Lorentzian products Sn×R1 or Hn×R1. This condition is expressed in terms of its first and second fundamental forms, the tangent and normal projections of the vectical vector field. As applications, we give an equivalent condition in a spinorial way and we deduce the...

Abstract. In this paper, we classify all the orientable hyperbolic 5-manifolds that arise as a hyperbolic space form H/Γ where Γ is a torsion-free subgroup of minimal index of the congruence two subgroup Γ 2 of the group Γ of positive units of the Lorentzian quadratic form x 1 + · · ·+ x 5 − x 6 . We also show that Γ 2 is a reflection group with respect to a 5-dimensional right-angled convex po...

We introduce a concept of distance for a space-time where the notion of point is replaced by the notion of physical states e.g. probability distributions. We apply ideas of information theory and compute the Fisher information matrix on such a space-time. This matrix is the metric on that manifold. We apply these ideas to a simple model and show that the Lorentzian metric can be obtained if we ...

Restrictions are obtained on the topology of a compact divergence-free null hypersurface in a four-dimensional Lorentzian manifold whose Ricci tensor is zero or satisfies some weaker conditions. This is done by showing that each null hypersurface of this type can be used to construct a family of three-dimensional Riemannian metrics which collapses with bounded curvature and applying known resul...

Compactification can control chaotic Mixmaster behavior in gravitational systems with p–form matter: we consider this in light of the connection between supergravity models and Kac–Moody algebras. We show that different compactifications define “mutations” of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems ...

Minkowski Space is the simplest four-dimensional Lorentzian Manifold, being topologically trivial and globally flat, and hence the simplest model of spacetime—from a General-Relativistic point of view. But this does not mean that it is altogether structurally trivial. In fact, it has a very rich structure, parts of which will be spelled out in detail in this contribution, which is written for M...

We consider the (massless) scalar field on a two-dimensional manifold with metric that changes signature from Lorentzian to Euclidean. Requiring a conserved momentum in the spatially homogeneous case leads to a particular choice of propagation rule. The resulting mix of positive and negative frequencies depends only on the total (conformal) size of the spacelike regions and not on the detailed ...