The main result of this paper is that a Lorentzian manifold is locally conformally equivalent to a manifold with recurrent lightlike vector field and totally isotropic Ricci tensor if and only if its conformal tractor holonomy admits a 2-dimensional totally isotropic invariant subspace. Furthermore, for semi-Riemannian manifolds of arbitrary signature we prove that the conformal holonomy algebr...

Spectral features induced by 45 in-plane misoriented grains have been observed in the far infrared magneto-transmission of YBa2Cu3O7−δ thin films. Two strong dispersive features are found at 80 and 160 cm−1 and a weaker one at 116 cm−1. The data can be well represented by Lorentzian oscillator contributions to the conductivity. Several possible interpretations are discussed. We conclude that th...

Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly by a globally hyperbolic spacetime admits a timelike closed geodesic, if some natural topological assumptions (fulfilled, for example, if one of the conjuga...

In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian metrics with all possible connected holonomy groups is obtained. As the applications, the Einstein equation, Lorentzian manifolds with parallel and recurrent spinor fields, conformally flat Walker met...

We investigate the twistor space and the Grassmannian fibre bundle of a Lorentzian 4-space with natural almost optical structures and its induced CR-structures. The twistor spaces of the Lorentzian space forms R 4 1, S 4 1 and H 4 1 are explicitly discussed. The given twistor construction is applied to surface theory in Lorentzian 4-spaces. Immersed spacelike surfaces in a Lorentzian 4-space wi...

in this paper, we study spacelike dual biharmonic curves. we characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the lorentzian dual heisenberg group . we give necessary and sufficient conditions for spacelike dual biharmonic curves in the lorentzian dual heisenberg group . therefore, we prove that all spacelike dual biharmonic curves are spacelike dual heli...

We study the problem of a temporal discontinuity in permittivity an unbounded medium with Lorentzian dispersion. More specifically, we tackle situation which monochromatic plane wave forward-traveling (generally lossy) Lorentzian-like scatters from interface that results instantaneous and homogeneous abrupt change its plasma frequency (while keeping resonance constant). In order to achieve mome...

The implementation of the Debye, narrowband Lorentzian, and wideband Lorentzian dielectric and magnetic media in the numerical tool EZ-FDTD developed at the University of Missouri-Rolla (UMR is described. This tool allows efficient and robust full-wave finite-difference time-domain modeling of different complex electromagnetic structures. Algorithms for dispersive media use the linear recursive...

By using variational methods, we study the existence and multiplicity of trajec-tories under a vectorial potential on (standard) stationary Lorentzian manifolds possibly with boundary. 1. Introduction and statement of the results. The pair (ᏸ,g) is called Lorentzian manifold if ᏸ is a connected finite-dimensional smooth manifold with dim ᏸ ≥ 2 and g is a Lorentzian metric on ᏸ, that is, g is a ...