A non-linear gravitational model with a multidimensional geometry and quadratic scalar curvature is considered. For certain parameter ranges, the extra dimensions are stabilized if the internal spaces have negative constant curvature. As a consequence, the 4–dimensional effective cosmological constant as well as the bulk cosmological constant become negative. The homogeneous and isotropic exter...

Combining analytic calculations, computer simulations, and classical density functional theory we determine the interfacial tension of orientable two-dimensional hard rectangles near a curved hard wall. Both a circular cavity holding the particles and a hard circular obstacle surrounded by particles are considered. We focus on moderate bulk densities (corresponding to area fractions up to 50%) ...

In this article we describe the formulation of null geodesics as null conformal geodesics and their description in the tractor formalism. A conformal extension theorem through an isotropic singularity is proven by requiring the boundedness of the tractor curvature and its derivatives to sufficient order along a congruence of null conformal geodesic. This article extends earlier work by Tod and ...

In this paper the Einstein-Vlasov system of self-consistent field equations is used to construct a cosmological model. A solution is found for a homogeneous isotropic space-time with positive curvature (R × S 3 topology). For the Universe consisting of massless particles the equation for R(t) is solved analytically.

We consider a task of tracing out target figures hidden in teeming figure pictures come to known as Wimmelbild(er). Wimmelbild is a popular genre of visual puzzles; a timeless classic for children, artists and cognitive scientists. Particularly suited to the considered task, we propose a diffuse representation which serves as a heuristic approximation mimicking curvature coding distance images....

1. Background. It is a fundamental goal in Riemannian geometry to understand the topology of manifolds of positive curvature. The only general facts so far known are: finiteness of fundamental group (Myers’ theorem), vanishing of Â-genus (Lichnerowicz’ theorem and the modification of Hitchin) and a universal bound on Betti numbers (Gromov’s theorem). In a well-known paper [10] Micallef and Moor...

An oscillating, homogeneous and isotropic Universe which arises from Scalar-Tensor gravity is discussed in the linearized approach, showing that some observative evidences like the Hubble Law and the Cosmological Redshift are in agreement with the model. In this context Dark Energy appears like a pure curvature effect arising by the scalar field. PACS numbers: 04.80.Nn, 04.30.Nk, 04.50.+h

We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem along a congruence of time-like conformal geodesics.

Non-minimally coupling a scalar field to gravity introduces an additional curvature term into the action which can change the general behavior in strong curvature regimes, in particular close to classical singularities. While one can conformally transform any non-minimal model to a minimally coupled one, that transformation can itself become singular. It is thus not guaranteed that all qualitat...