Almost-Riemann solitons are introduced and studied on an almost contact complex Riemannian manifold, i.e., almost-contact B-metric which is obtained from a cosymplectic manifold of the considered type by means conformal transformation Reeb vector field, its dual 1-form, B-metric, associated B-metric. The potential soliton assumed to be in vertical distribution, it collinear field. In this way, ...

The conformal method for constructing initial data for Einstein’s equations is presented in both the Hamiltonian and Lagrangian picture (extrinsic curvature decomposition and conformal thin sandwich formalism, respectively), and advantages due to the recent introduction of a weight-function in the extrinsic curvature decomposition are discussed. I then describe recent progress in numerical tech...

Abstract Symmetries play an important role in fundamental physics. In gravity and field theories, particular attention has been paid to Weyl (or conformal) symmetry. However, once the theory contains a scalar field, conformal transformations of metric can be considered subclass more general type transformation, so-called disformal transformation. Here, we investigate implications pure symmetry ...

We consider the unit tangent sphere bundle of Riemannian manifold ( M, g ) with g-natural metric G̃ and we equip it to an almost contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of ( M, g ) and local symmetry property of G̃. More precisely, we prove that the flatness of metric g is necessary and sufficien...

The paper aims to investigate curvature inheritance (CI) symmetry in M-projectively flat spacetimes. It is shown that the CI spacetime a conformal motion. We have proved M-projective tensor follows property along vector field ξ, when admits conditions of both and motion or ξ. Also, we derived some results for with perfect fluid following Einstein equations (EFEs) cosmological term admitting an ...

the general relatively isotropic mean landsberg metrics contain the general relativelyisotropic landsberg metrics. a class of finsler metrics is given, in which the mentioned two conceptsare equivalent. in this paper, an interpretation of general relatively isotropic mean landsberg metrics isfound by using c-conformal transformations. some necessary conditions for a general relativelyisotropic ...

The conformal anomaly induced sector of four-dimensional quantum gravity (infrared quantum gravity) —which has been introduced by Antoniadis and Mottola— is here studied on a curved fiducial background. The one-loop effective potential for the effective conformal factor theory is calculated with accuracy, including terms linear in the curvature. It is proven that a curvature induced phase trans...

Conformal fields are a new class of V ect(N) modules which are more general than tensor fields. The corresponding diffeomorphism group action is constructed. Conformal fields are thus invariantly defined. PACS numbers: 02.20, 02.40

In logarithmic conformal field theory, primary fields come together with logarithmic partner fields on which the stress-energy tensor acts non-diagonally. Exploiting this fact and global conformal invariance of two-and three-point functions, operator product expansions of logarithmic operators in arbitrary rank logarithmic conformal field theory are derived.

1. The notion of a "curvature structure" was introduced in §8, Chapter 1 of [ l ] . In this note we shall consider some of its applications. The details will be presented elsewhere. Let (M, g) be a Riemann manifold. Whenever convenient, we shall denote the inner product defined by g, by ( ). DEFINITION. A curvature structure on (M, g) is a (1, 3) tensor field T such that, for any vector fields ...