In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

We study the limiting behavior of the zeros of the Euler polynomials. When linearly scaled, they approach a definite curve in the complex plane related to the Szegö curve which governs the behavior of the roots of the Taylor polynomials associated to the exponential function. Further, under a conformal transformation, the scaled zeros are uniformly distributed.

We introduce an orbifold induction procedure which provides a systematic construction of cyclic orbifolds, including their twisted sectors. The procedure gives counterparts in the orbifold theory of all the current-algebraic constructions of conformal field theory and enables us to find the orbifold characters and their modular transformation properties.

The change of conformal moduli of polygonal quadrilaterals under some geometric transformations is studied. We consider the motion of one vertex when the other vertices remain fixed, the rotation of sides, polarization, symmetrization, and averaging transformation of the quadrilaterals. Some open problems are formulated. 2000 Mathematics Subject Classification. Primary 30C85. Secondary 30C75.

Spectral indices from models of inflation which incorporate a Generalized Einstein Theory (GET) gravity sector are calculated to first order in a slow-roll expansion. By quantizing a suitably-generalized measure of the intrinsic curvature perturbation, the spectral indices as calculated in the Jordan frame now match those as calculated following a conformal transformation, in the Einstein frame...

In this paper the geometry of two-qubit systems under local unitary group SO(2) ⊗ SU(2) is discussed. It is shown that the quaternionic conformal map intertwines between this local unitary subgroup of Sp(2) and the quaternionic Möbius transformation which is rather a generalization of the results of Lee et al (2002 Quantum Inf. Process. 1 129).

We show that the behaviour of the outgoing radial null geodesic congruence on the boundary of the trapped region (suitably defined as a four dimensional region) is related to the property of nakedness in spherical dust collapse. The argument involves a conformal transformation which justifies the difference in the Penrose diagrams in the naked and covered dust collapse scenarios.

We investigate whether the gravitational thermodynamic properties of the scalar-tensor theory of gravity are affected by the conformal transformation or not. As an explicit example, we consider an electrically charged static spherical black hole in the 4-dimensional low energy effective theory of bosonic string. E-mail address : [email protected] E-mail address : [email protected]. ...

We analyze the operator product expansion Tμν(z)W [C] in N = 4 4-dimensional Super-Yang-Mills(SYM) theory with U(N) gauge group, and clarify that the closed Wilson loop does not possess an anomalous dimension and that only the shape of the loop is changed by the conformal transformation.