For a given finite subset S of compact Riemannian manifold (M,g) whose Schouten curvature tensor belongs to cone, we establish necessary and sufficient condition for the existence uniqueness conformal metric on M\S such that each point corresponds an asymptotically flat end boundary cone. As by-product, define purely local notion Ricci lower bounds continuous metrics are smooth prove correspond...

In this paper we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure-radiation type and that it restricts the spacetimes to Petrov types N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with...

Higher-curvature corrections to the effective gravitational action may leave signatures in spectrum of primordial tensor perturbations if inflationary energy scale is sufficiently high. In this paper, we further investigate effects a coupling Inflaton field higher-curvature tensors models with minimal breaking conformal symmetry. We show that an observable violation consistency relation from im...

One of the most important problem in conformal geometry is the construction of conformal metrics for which a certain curvature quantity equals a prescribed function, e.g. a constant. In two dimensions, the problem of prescribed Gaussian curvature asks the following: given a smooth function K on (M,g0), can we find a metric g conformal to g0 such that K is the Gaussian curvature of the new metri...

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.

This article presents a new definition of Branson’s Q-curvature in even dimensional conformal geometry. The Q-curvature is a generalization of the scalar curvature in dimension 2: it satisfies an analogous transformation law under conformal rescalings of the metric and on conformally flat manifolds its integral is a multiple of the Euler characteristic. Our approach is motivated by the recent w...

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...

Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...

We calculate the anisotropies in the cosmic microwave background induced by long-wavelength primordial gravitational waves in a universe with negative spatial curvature, such as are produced in the “open inflation” scenario. The impact of these results on the COBE normalization of open models is discussed. Subject headings: cosmology:theory – cosmic microwave background There is considerable ob...

This paper presents a method to compute the quasi-conformal parameterization (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain S onto a punctured disk DS associated with a given Beltrami differential. The Beltrami differential, which measures the conformality distortion, is a complexvalued function μ : S → C with supremum ...