Prescribing, by conformal transformation, the k-elementary symmetric polynomial of the Schouten tensor σk(P) to be constant is a generalisation of the Yamabe problem. On compact Riemannian n-manifolds we show that, for 3 ≤ k ≤ n, this prescription equation is an Euler-Lagrange equation of some action if and only if the structure is locally conformally flat.

Let A be a positive integral power of a natural, conformally covariant diierential operator on tensor-spinors in a Riemannian manifold. Suppose that A is formally self-adjoint and has positive deenite leading symbol. For example, A could be the conformal Laplacian (Yamabe operator) L, or the square of the Dirac operator r =. Within the conformal class fg = e 2w g 0 j w 2 C 1 (M)g of an Einstein...

An overview of the transformation electromagnetics/optics design technique is presented. Illustrative example designs for invisibility cloaks, beam control devices, lenses as well as applications to radiation problems are shown. Quasi-conformal transformations in two dimensions and their applications to cloaks and virtual arrays are discussed.

In the context of modified gravity, we point out how the Palatini version of these theories is singled out as a very special case corresponding to the unique fixed point of a transformation involving a special conformal rescaling of the metric. This mathematical peculiarity signals deeply rooted problems which make the theory unphysical. PACS: 04.50+h, 04.20.Cv, 04.20.Fy, 04.90.+e.

The one-loop contributions to the entropy for a massive scalar field in a Kerr black hole are investigated using an approximation of the metric, which, after a conformal transformation, permits to work in a Rindler-like spacetime. Of course, as for the Schwarzschild case, the entropy is divergent in the proximity of the event horizon. PACS numbers: 04.62.+v, 04.70.Dy

Transformation optics has been used to propose various novel optical devices. With the help of metamaterials, several intriguing designs, such as invisibility cloaks, have been implemented. However, as the basic units should be much smaller than the working wavelengths to achieve the effective material parameters, and the sizes of devices should be much larger than the wavelengths of illuminati...

We investigate the superconformal transformation properties of the supercurrent as well as of the superconformal anomalies themselves in d = 4, N = 1 supersymmetric quantum field theory. Matter supercurrent and anomalies are coupled to a classical background of minimal supergravity fields. On flat superspace, there exist two different types of the superconformal Ward identity (called S and B) w...

An inversion procedure, based on the methods used in proving Btirmasm’s theorem, is used to provide an integral expression which exhibits the form of the electrostatic field explicitly in terms of the field coordinates. The method is illustrated with an example of a stepped-guide junction. The form of the field and the expression for the mode expansion coefficients are examined. The results are...

In this paper we present a conformal mapping-based approach for 3D face recognition. The proposed approach makes use of conformal UV parameterization for mapping purpose and Shape Index decomposition for similarity measurement. Indeed, according to conformal geometry theory, each 3D surface with disk topology can be mapped onto a 2D domain through a global optimization, resulting in a diffeomor...

When setting up global ocean circulation models one faces the problem of including the Arctic Ocean where the traditional spherical coordinate system has a singularity at the pole. In addition, in regional model applications one has to deal with open boundaries where assumptions are made about the normally poorly known boundary conditions. Here an analytical reversible coordinate transformation...