The goal of the present paper is to investigate the algebraic structure of global conformal invariants of submanifolds. These are defined to be conformally invariant integrals of geometric scalars of the tangent and normal bundle. A famous example of a global conformal invariant is the Willmore energy of a surface. In codimension one we classify such invariants, showing that under a structural ...

We consider 5-dimensional spacetimes of constant 3-dimensional spatial curvature in the presence of a bulk cosmological constant. We find the general solution of such a configuration in the presence of a Gauss-Bonnet term. Two classes of non-trivial bulk solutions are found. The first class is valid only under a fine tuning relation between the Gauss-Bonnet coupling constant and the cosmologica...

The local and global thermal phase structure for asymptotically anti-de Sitter black holes charged under an abelian gauge group, with both Gauss-Bonnet and quartic field strength corrections, is mapped out for all parameter space. We work in the grand canonical ensemble where the external electric potential is held fixed. The analysis is performed in an arbitrary number of dimensions, for all t...

Earlier we constructed a model with exponential form potential and of Gauss–Bonnet interaction. This can be considered as an appropriate inflationary scenario. In this model, the attractor parameters correspond to ones from cosmological in leading order approximation inverse e-folding number. We study how many orders numbers are included spectral index scenario Einstein–Gauss–Bonnet gravity.

We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in wide class of modified theories gravity. The utilizes relaxed Newton-Raphson method solve the full nonlinear Einstein's equations on two-dimensional grid with Newton polynomial finite difference scheme. validate this by considering static and holes general r...

In this paper we construct a version of Ricci flow for noncommutative 2-tori, based on a spectral formulation in terms of the eigenvalues and eigenfunction of the Laplacian and recent results on the Gauss–Bonnet theorem for noncommutative tori.

We introduce a metric notion of Ricci curvature for PL manifolds and study its convergence properties. We also prove a fitting version of the Bonnet-Myers Theorem, for surfaces as well as for a large class of higher dimensional manifolds.