Comparing the location and size of functional brain activity across subjects is difficult due to individual differences in folding patterns and functional foci are often buried within cortical sulci. Cortical flat mapping is a tool which can address these problems by taking advantage of the two-dimensional sheet topology of the cortical surface. Flat mappings of the cortex assist in simplifying...

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...

In this paper we present a simple method for flattening of triangulated surfaces for mapping and imaging. The method is based on classical results of F. Gehring and Y. Väisälä regarding the existence of quasi-conformal and quasi-isometric mappings between Riemannian manifolds. A random starting triangle version of the algorithm is presented. A curvature based version is also applicable. In addi...

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.

In studying temperature fluctuations in the cosmic microwave background Weinberg has noted that some ease of calculation and insight can be achieved by looking at structure perturbed light cone on which photons propagate. his approach worked a specific gauge specialized to around standard Robertson-Walker cosmological model with vanishing spatial three-curvature. this paper we generalize analys...