A novel method for designing a signature based on the conformal mapping is proposed. Conformal mapping function preserves the local angles of the shape of the object. Schwarz Christoffel mapping transformation is effectively implemented. A conformal transformation of the upper half plane onto the interior of a simple polygon is carried out. The widely used in 2-D potential flow for the computat...

In a study of Riemannian manifolds admitting conformal transformation, the Riemannian and Ricci curvatures play an important role for characterizations and classify such a manifold. In this note, we summarize known results about Riemannian manifold admitting conformal transformations and related topics.

A gauge transformation in quantum electrodynamics involves the product of field operators at the same space-time point and hence does not have a well-defined meaning. One way to avoid this difficulty is to generalize the gauge transformation by using different space-time points in the spirit of Dirac's point splitting. Such a generalization indeed exists and the resulting generalized infinitesi...

We study logarithmic conformal field theories (LCFTs) through the introduction of nilpotent conformal weights. Using this device, we derive the properties of LCFT’s such as the transformation laws, singular vectors and the structure of correlation functions. We discuss the emergence of an extra energy momentum tensor, which is the logarithmic partner of the energy momentum tensor. PACS: 11.25.Hf

Abstract. In this paper, we have studied a conformal transformation between two almost Hermitian manifolds and shown that the associated Nijenhuis tensor is conformally invariant under this transformation. We have also discussed the properties of contravariant almost analytic vector field, covariant almost analytic vector field and some other properties in almost Hermitian manifold under this t...

A natural geometry, arising from the embedding into a Hilbert space of the parametrised probability measure for a given lattice model, is used to study the symmetry properties of real-space renormalisation group (RG) flow. In the projective state space this flow is shown to have two contributions: a gradient term, which generates a projective automorphism of the state space for each given lengt...

We investigate two-dimensional dilaton gravity models with a power-law dilaton potential, whose black hole solutions contain, among others, the dimensional reduction of the Schwarzschild black hole, the Anti-de Sitter black hole and Rindler spacetime. We show that the ground state of these models satisfies simple transformation laws under the SL(2, R) conformal group. We use these transformatio...