In this paper, first we give a notion for linear Weingarten spacelike hypersurfaces with P + aH = b in a locally symmetric Lorentz space Ln+1 1 . Furthermore, we study complete or compact linear Weingarten spacelike hypersurfaces in locally symmetric Lorentz spaces Ln+1 1 satisfying some curvature conditions. By modifying Cheng-Yau’s operator given in [7], we introduce a modified operator L and...

We show that if one takes into account Penrose’s conformal technique in the Einstein-Cartan gravity, it is possible to obtain a relation between Hubble’s expansion and Birch’s rotation of the Universe at spacelike infinity. This relation also leads to the final reduction of the gravitational coupling to a dimensionless quantity of order unity at spacelike infinity. Initial-value equations at sp...

Pseudo-Riemannian manifolds of balanced signature which are both spacelike and timelike Jordan Osserman nilpotent of order 2 and of order 3 have been constructed previously. In this short note, we shall construct pseudo-Riemannian manifolds of signature (2s, s) for any s ≥ 2 which are spacelike Jordan Osserman nilpotent of order 3 but which are not timelike Jordan Osserman. Our example and tech...

According to the Borde-Guth-Vilenkin (BGV) theorem an expanding region of spacetime cannot be extended past beyond some boundary \mathcal{B}. Therefore, inflationary universe must have had kind beginning. However, BGW says nothing about conditions on \mathcal{B}, or even its location. Here we present a single-scalar field model Two-Measure Theory, where non-Riemannian volume element $\Upsilon d...

We develop an extension of Bohmian mechanics by defining Bohm-like tra-jectories for quantum particles in a curved background space-time containing a spacelike singularity. As an example of such a metric we use the Schwarzschild metric, which contains two spacelike singularities, one in the past and one in the future. Since the particle world lines are everywhere timelike or lightlike, particle...

Causality requires that the ~anti!commutator of two interacting field operators vanishes for spacelike coordinate differences. This implies that the Fourier transform of the spectral function of this quantum field should vanish in the spacelike domain. We find that this requirement imposes some constraints on the use of resummed propagators in high temperature gauge theory. @S0556-2821~96!02418-6#

‎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 ‎$mathbb{L}^{2}.$‎

In this paper we introduce the notion of pseudo-spherical evolutes of curves on a spacelike surface in three dimensional Lorentz-Minkowski space which is analogous to the notion of evolutes of curves on the hyperbolic plane. We investigate the the singularities and geometric properties of pseudo-spherical evolutes of curves on a spacelike surface.

Let N p (c) be an (n+p)-dimensional connected Lorentzian space form of constant sectional curvature c and φ : M → N p (c) an n-dimensional spacelike submanifold in N p (c). The immersion φ : M → N p (c) is called a Willmore spacelike submanifold in N p (c) if it is a critical submanifold to the Willmore functional W (φ) = ∫