The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2, 1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is completely determined. Essentially, the solutions are warped products of orbits of the 1-dimensional groups of isometries and elastic curves in either a de...

In this paper we present an existence and multiplicity result for periodic trajectories on stationary Lorentzian manifolds, possibly with boundary, whose proof is based on a Morse theory approach, see [5]. We recall that a Lorentzian manifold is a smooth connected nite-dimensional manifold M equipped with a (0; 2) tensor eld g such that for any z ∈ M g(z) [·; ·] is a nondegenerate symmetric bil...

We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or CH3 for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, CH2 manifolds that are not homogeneous. The resulting metrics belong to the class of null electromagnetic radiation, type N solutions on an anti-de Sitter background. These findings prove th...

We investigate connections between pairs of (pseudo-)Riemannian metrics whose sum is a (tensor) product of a covector field with itself. A bijective mapping between the classes of Euclidean and Lorentzian metrics is constructed as a special result. The existence of such maps on a differentiable manifold is discussed. Similar relations for metrics of arbitrary signature on a manifold are conside...

Penrose’s spinor calculus of four-dimensional Lorentzian geometry is extended to the case of five-dimensional Lorentzian geometry. Such fruitful ideas in Penrose’s spinor calculus as the spin covariant derivative, the curvature spinors, or the definition of the spin coefficients on a spin frame can be carried over to the spinor calculus in five-dimensional Lorentzian geometry. The algebraic and...

We give a Lorentzian metric on the null congruence associated with a timelike conformal vector field. A Liouville type theorem is proved and a boundedness for the volume of the null congruence, analogous to a well-known Berger-Green theorem in the Riemannian case, will be derived by studying conjugate points along null geodesics. As a consequence, several classification results on certain compa...

Numerical solutions of the Kadanoo{Baym equations with selfenergies in second Born approximation are presented for electrons in a bulk semiconductor. The results are used to analyze in detail the two{time spectral function A(tt 0). In particular, (I) the damping of the spectral function is investigated over a broad density range both, for low and high temperatures; (II), A(tt 0) is compared to ...