If the holonomy representation of an (n + 2)–dimensional simply-connected Lorentzian manifold (M,h) admits a degenerate invariant subspace its holonomy group is contained in the parabolic group (R×SO(n))⋉R. The main ingredient of such a holonomy group is the SO(n)–projection G := prSO(n)(Holp(M,h)) and one may ask whether it has to be a Riemannian holonomy group. In this paper we show that this...

We analyze the renormalization properties of quantum field theories in de Sitter space and show that only two of the maximally invariant vacuum states of free fields lead to consistent perturbation expansions. One is the Euclidean vacuum and the other can be viewed as an analytic continuation of Euclidean functional integrals on RP . The corresponding Lorentzian manifold is the future half of g...

We compute the Green’s function for the Hodge Laplacian on the symmetric spaces M × Σ, where M is a simply connected n-dimensional Riemannian or Lorentzian manifold of constant curvature and Σ is a simply connected Riemannian surface of constant curvature. Our approach is based on a generalization to the case of differential forms of the method of spherical means and on the use of Riesz distrib...

We consider a non-trapping n-dimensional Lorentzian manifold endowed with an end structure modeled on the radial compactification of Minkowski space. We find a full asymptotic expansion for tempered forward solutions of the wave equation in all asymptotic regimes. The rates of decay seen in the asymptotic expansion are related to the resonances of a natural asymptotically hyperbolic problem on ...

Together with spaces of constant sectional curvature and products of a real line with a manifold of constant curvature, the socalled Egorov spaces and ε-spaces exhaust the class of n-dimensional Lorentzian manifolds admitting a group of isometries of dimension at least 1 2n(n − 1) + 1, for almost all values of n [Patrangenaru V., Geom. Dedicata 102 (2003), 25–33]. We shall prove that the curvat...

I feel honoured to be able to make this small contribution to the celebration of Jerzy Plebański’s 75th birthday. Plebański has presumably regarded his work on complex relativity as a step towards producing general solutions to the Einstein equations on a real Lorentzian manifold. No one in the mid-seventies could expect that his contributions to the field would underlie the relation between tw...

It is shown that, on a manifold with a Finsler metric of Lorentzian signature, the lightlike geodesics satisfy the following variational principle. Among all lightlike curves from a point q (emission event) to a timelike curve γ (worldline of receiver), the lightlike geodesics make the arrival time stationary. Here “arrival time” refers to a parametrization of the timelike curve γ. This variati...

‎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 article, we investigate anti-invariant Riemannian and Lagrangian submersions onto manifolds from the Lorentzian para-Sasakian manifold. We demonstrate that, for these submersions, horizontal distributions are not integrable their fibers totally geodesic. As a result, they geodesic maps. The harmonicity of such is also examined. specifically prove that harmonic when Reeb vector field hor...

It is shown that every regular electromagnetic field in vacuum identically satisfy Maxwell equations a new manifold where the roles of space and time have been exchanged. The metric Lorentzian, depends on particular solution forces flow to tilt somehow direction lines. We give detailed description transformation discuss several its properties, both algebraic differential settings. Examples are ...