Abstract The dominant energy condition imposes a restriction on initial value pairs found spacelike hypersurface of Lorentzian manifold. In this article, we study the space values that satisfy strictly. To aim, introduce an index difference for and compare it to its classical counterpart Riemannian metrics. Recent non-triviality results latter will then imply has non-trivial homotopy groups.

Let M be a connected, simply oriented, closed, smooth four-manifold which is spin (or equivalently having even intersection form) and put M×?M?{point}. In this paper we prove that if X× homeomorphic but not necessarily diffeomorphic to M× (more precisely, it carries structure à la Gompf) then can equipped with complete Ricci-flat Riemannian metric. As byproduct of the construction follows metri...

the present paper is concerned with the generalization of the holditch theorem under oneparameterhomothetic motion on lorentzian planes. in this paper, for the homothetic lorentzian motion, weexpressed the steiner formula. furthermore, we present the holditch-type theorems.

In this paper, we consider Lorentzian para-Kenmotsu manifold admitting almost $\eta-$Ricci solitons by virtue of some curvature tensors. Ricci pseudosymmetry concepts manifolds soliton have introduced according to the choice tensors such as Riemann, concircular, projective, $\mathcal{M-}$projective, $W_{1}$ and $W_{2}.$ After then, tensors, necessary conditions are given for be semisymmetric. T...

This talk will deal to a certain extent with the natural continuation of some work in progress that was introduced last year at the Spanish Relativity Meeting in Salamanca 1, 2 and that has recently been published 3. The reason for investigating geodesic completeness of Lorentzian manifolds is twofold. From the mathematical point of view, there is no analogue for the Hopf-Rinow theorem that cha...

Two-dimensional Lorentzian geometry has recently found application in some models of nonrelativistic systems, most profitably for the process of boarding an aeroplane. The duration of the boarding process is assumed to be a result of passengers standing in the isle and blocking each others’ way. According to this model, the expected boarding time is equal to the length of the longest timelike g...

‎In this work‎, ‎first the differential equation characterizing position vector‎ ‎of spacelike curve is obtained in Lorentzian plane $mathbb{L}^{2}.$ Then the‎ ‎special curves mentioned above are studied in Lorentzian plane $mathbb{L}%‎‎^{2}.$ Finally some characterizations of these special curves are given in‎ ‎$mathbb{L}^{2}.$‎

For a canonical formulation of quantum gravity, the superspace of all possible 3-geometries on a Cauchy hypersurface of a 3 + 1-dimensional Lorentzian manifold plays a key role. While in the analogous 2 + 1-dimensional case the superspace of all Riemannian 2-geometries is well known, the structure of the superspace of all Riemannian 3-geometries has not yet been resolved at present. In this pap...