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...

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 a...

We prove a Pohozaev type identity for non-linear eigenvalue equations of the Dirac operator on Riemannian spin manifolds with boundary. As an application, we obtain that the mean curvature H of a conformal immersion S → R satisfies ∫ ∂XH = 0 where X is a conformal vector field on S and where the integration is carried out with respect to the Euclidean volume measure of the image. This identity ...

We show that conformal manifolds in $d\geq 3$ field theories with at least 4 supercharges are K\"ahler-Hodge, thus extending to 3d ${\cal N}=2$ and 4d N}=1$ similar results previously derived for N}=4$ various types of 2d SCFTs. Conformal SCFTs equipped a holomorphic line bundle L}$, which encodes the operator mixing under marginal deformations. Using perturbation theory superconformal Ward ide...

Recently, various conformal geometric methods have been presented for non-rigid surface matching and registration. This work proposes to improve the robustness of conformal geometric methods to the boundaries by incorporating the symmetric information of the input surface. We presented two symmetric conformal mapping methods, which are based on solving Riemann-Cauchy equation and curvature flow...

The Paneitz operator is a fourth order differential operator which arises in conformal geometry and satisfies a certain covariance property. Associated to it is a fourth order curvature – the Qcurvature. We prove the existence of a continuum of conformal radially symmetric complete metrics in hyperbolic space Hn, n > 4, all having the same constant Q-curvature. Moreover, similar results can be ...

we classify the paracontact riemannian manifolds that their rieman-nian curvature satisfies in the certain condition and we show that thisclassification is hold for the special cases semi-symmetric and locally sym-metric spaces. finally we study paracontact riemannian manifolds satis-fying r(x, ξ).s = 0, where s is the ricci tensor.