We include the brane curvature scalar to study its cosmological implication in the brane world cosmology. This term is usually introduced to obtain the well-defined stress-energy tensor on the boundary of anti de Sitter-Schwarzschild space. Here we treat this as the perturbed term for cosmological purpose. It is shown that the brane curvature scalar induces some interesting consequences in the ...

In this paper we study Riemannian manifolds (M, g) equipped with a smooth measure m. In particular, we show that the construction of conformally covariant operators due to Graham-Jenne-Mason-Sparling can be adapted to this setting. As a by-product, we define a family of scalar curvatures, one of which corresponds to Perelman’s scalar curvature function. We also study the variational problem nat...

We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the conformal Ricci flow equations because of the role that conformal geometry plays in constraining the scalar curvature and because these equations are the vector field sum of a conformal flow equation and a...

We investigate the possibility of dressing a four-dimensional black hole with classical scalar field hair which is non-minimally coupled to the space-time curvature. Our model includes a cosmological constant but no self-interaction potential for the scalar field. We are able to rule out black hole hair except when the cosmological constant is negative and the constant governing the coupling to...

Abstract. Given a collection of N asymptotically Euclidean ends with zero scalar curvature, we construct a Riemannian manifold with zero scalar curvature and one asymptotically Euclidean end, whose boundary has a neighborhood isometric to the disjoint union of a specified collection of sub-regions of the given ends. An application is the construction of time-symmetric solutions of the constrain...

Let (M,J) be a compact complex 2-manifold which which admits a Kähler metric for which the integral of the scalar curvature is nonnegative. Also suppose that M does not admit a Ricci-flat Kähler metric. Then if M is blown up at sufficiently many points, the resulting complex surface (M̃ , J̃) admits Kähler metrics with scalar curvature identically equal to zero. This proves Conjecture 1 of [16]. ...

An exact four-dimensional black hole solution of gravity with a minimally coupled self-interacting scalar field is reported. The event horizon is a surface of negative constant curvature enclosing the curvature singularity at the origin, and the scalar field is regular everywhere outside the origin. This solution is an asymptotically locally AdS spacetime. The strong energy condition is satisfi...

It is a simple consequence of the maximum principle that a superharmonic function u on Rn(i. e. ∆u ≤ 0) which is 1 near infinity is identically 1 on Rn (throughout this paper, n ≥ 3). Geometrically this means that one can not conformally deform the Euclidean metric in a bounded region without decreasing the scalar curvature somewhere. In fact there is a much stronger result: one can not have an...

Let (M, g) be a compact Riemannian manifold of dimension n ≥ 3 with boundary ∂M . We denote the Ricci curvature, scalar curvature, mean curvature, and the second fundamental form by Ric, R , h, and Lαβ , respectively. The Yamabe problem for manifolds with boundary is to find a conformal metric ĝ = eg such that the scalar curvature is constant and the mean curvature is zero. The boundary is call...

We present a computational study of the transport properties of campylotic (intrinsically curved) media. It is found that the relation between the flow through a campylotic media, consisting of randomly located curvature perturbations, and the average Ricci scalar of the system, exhibits two distinct functional expressions, depending on whether the typical spatial extent of the curvature pertur...