We obtain cosmological solutions which admit emergent universe (EU) scenario in four dimensions in the framework of Einstein Gauss-Bonnet gravity coupled with a dilaton field. We determine the coupling parameter of the Gauss-Bonnet terms and the dilaton to obtain EU scenario. The corresponding dilaton potential is obtained. It is found that the Gauss-Bonnet (GB) terms coupled with dilaton field...

We study static black hole solutions in Einstein and Einstein–Gauss–Bonnet gravity with the topology of the product of two spheres,Sn × Sn, in higher dimensions. There is an unusual new feature of the Gauss–Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of > 0. For an Einstein–Gauss–Bonnet black hole a limited window of ne...

We study the thermodynamic properties associated with black hole horizon and cosmological horizon for the Gauss-Bonnet solution in de Sitter space. When the Gauss-Bonnet coefficient is positive, a locally stable small black hole appears in the case of spacetime dimension d = 5, the stable small black hole disappears and the Gauss-Bonnet black hole is always unstable quantum mechanically when d ...

In this paper, we survey recent results on Gauss-Bonnet-Chern formulae and related issues for closed Riemannian manifolds with variable curvature. Among other things, we address the following problem: “if M is an oriented 2n-dimensional closed manifold with non-positive curvature, then is it true that its Euler number χ(M) satisfies the inequality (−1)χ(M) ≥ 0?” We will present some partial ans...

We study thermodynamic properties and phase structures of topological black holes in Einstein theory with a Gauss-Bonnet term and a negative cosmological constant. The event horizon of these topological black holes can be a hypersurface with positive, zero or negative constant curvature. When the horizon is a zero curvature hypersurface, the thermodynamic properties of black holes are completel...

Constant mean curvature surfaces (abbriviated as CMC surfaces) in the space forms are typical examples of isothermic surfaces. Bonnet showed that every constant mean curvature surface admits a one-parameter family of isometric deformations preserving the mean curvature. A surface which admits such a family of deformations is called a Bonnet surface. Both the isothermic surfaces and Bonnet surfa...

Current Opinion in Ophthalmology 2009, 20:219–222 Purpose of review The aging of the population and the resultant increase in the number of patients with low vision due to age-related macular degeneration and other ocular diseases necessitate an increase in awareness of the Charles Bonnet syndrome among ophthalmic care providers. Recent findings The clinical features of Charles Bonnet syndrome ...

Bonnet surfaces, i.e. surfaces in Euclidean 3-space, which admits a one-parameter family of isometries preserving the mean curvature function, can be described in terms of solutions of some special Painlev e equations. The goal of this work is to use the well-known Schlesinger transformations for solutions of Painlev e VI equations to create new Bonnet surfaces from a known one.

mathematical techniques. When the "objects" considered have specific properties, it is possible to envisage (and even to recommend) how to exploit these properties for performing dimensionality reduction. One example of this approach consists in replacing images of centro-symmetric particles by their rotational power spectrum (Crowther and Amos, 1971): the image is split into angular sectors, t...

Radion stabilization is analyzed in 5–dimensional models with branes in the presence of Gauss–Bonnet interactions. The Goldberger–Wise mechanism is considered for static and inflating backgrounds. The necessary and sufficient conditions for stability are given for the static case. The influence of the Gauss–Bonnet term on the radion mass and the inter–brane distance is analyzed and illustrated ...