We deal with a 2m-dimensional Riemannian manifold (M,g) structured by an affine connection and a vector field , defining a -parallel connection. It is proved that is both a torse forming vector field and an exterior concurrent vector field. Properties of the curvature 2-forms are established. It is shown that M is endowed with a conformal symplectic structure Ω and defines a relative conformal ...

The initial-value problem is posed by giving a conformal three-metric on each of two nearby spacelike hypersurfaces, their proper-time separation up to a multiplier to be determined, and the mean (extrinsic) curvature of one slice. The resulting equations have the same elliptic form as does the one-hypersurface formulation. The metrical roots of this form are revealed by a conformal " thin sand...

We answer a question raised by M. Chuaqui, P. Duren, and B. Osgood by showing that a conformal mapping of a simply connected domain cannot take two circles onto two proper ellipses. The goal of this note is to prove the following. Proposition 1. Let Ω be a simply connected domain on C = C ∪ {∞} containing circles (on C) C1 and C2, C1 = C2. Let f be a conformal mapping from Ω into C. If f maps e...

The singularity present in cosmological instantons of the Hawking-Turok type is resolved by a conformal transformation, where the conformal factor has a linear zero of codimension one. We show that if the underlying regular manifold is taken to have the topology of RP 4, and the conformal factor is taken to be a twisted field so that the zero is enforced, then one obtains a genuine saddle point...

The previously analyzed holographic encoding of bulk matter is generalized from wedges to double cones. As a result of the conformal invariance of the holographically projected wedge-bulk matter, one may apply a conformal transformation in the ambient space which maps the holographic projection of the wedge into that of the double cone. In the massive case this conformal map cannot be used for ...

A contribution linear in r to the gravitational potential can be created by a suitable conformal duality transformation: the conformal factor is 1/(1 + r) and r will be replaced by r/(1 + r), where r is the Schwarzschild radial coordinate. Thus, every spherically symmetric solution of conformal Weyl gravity is conformally related to an Einstein space. This result finally resolves a long controv...

Conformal (Same form or shape) mapping is an important technique used in complex analysis and has many applications in different physical situations.If the function is harmonic (ie it satisfies Laplace’s equation∇f = 0 )then the transformation of such functions via conformal mapping is also harmonic. So equations pertaining to any field that can be represented by a potential function (all conse...

In gauge theories, not all rigid symmetries of the classical action can be maintained manifestly in the quantization procedure, even in the absence of anomalies. If this occurs for an anomaly-free symmetry, the effective action is invariant under a transformation that differs from its classical counterpart by quantum corrections. As shown by Fradkin and Palchik years ago, such a phenomenon occu...

In gauge theories, not all rigid symmetries of the classical action can be maintained manifestly in the quantization procedure, even in the absence of anomalies. If this occurs for an anomaly-free symmetry, the effective action is invariant under a transformation that differs from its classical counterpart by quantum corrections. As shown by Fradkin and Palchik years ago, such a phenomenon occu...

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 ...