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#

biharmonic surfaces in euclidean space $mathbb{e}^3$ are firstly studied from a differential geometric point of view by bang-yen chen, who showed that the only biharmonic surfaces are minimal ones. a surface $x : m^2rightarrowmathbb{e}^{3}$ is called biharmonic if $delta^2x=0$, where $delta$ is the laplace operator of $m^2$. we study the $l_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

We give a Hamiltonian definition of mass for spacelike hypersurfaces in space-times with metrics which are asymptotic to the anti-de Sitter one, or to a class of generalizations thereof. We show that our definition provides a geometric invariant for a spacelike hypersurface embedded in a space-time.

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) = ∫

We prove a global existence theorem (with respect to a geometricallydefined time) for globally hyperbolic solutions of the vacuum Einstein equations which admit a T 2 isometry group with two-dimensional spacelike orbits, acting on T 3 spacelike surfaces. Visiting Scientist: Max-Planck-Institut für Gravitationsphysik (Albert-EinsteinInstitut) Schlaatzweg 1, 14473 Potsdam, Germany

We give a Hamiltonian definition of mass for spacelike hypersurfaces in space-times with metrics which are asymptotic to the anti-de Sitter one, or to a class of generalizations thereof. We show that our definition provides a geometric invariant for a spacelike hypersurface embedded in a space-time.

Horocyclic surfaces are surfaces in hyperbolic 3-space that are foliated by horocycles. We construct horocyclic surfaces associated with spacelike curves in the lightcone and investigate their geometric properties. In particular, we classify their singularities using invariants of corresponding spacelike curves.