Related papers: A Weyl-covariant tensor calculus

A Weyl structure is usually defined by an equivalence class of pairs $({\bf g}, \boldsymbol{\omega})$ related by Weyl transformations, which preserve the relation $\nabla {\bf g}=\boldsymbol{\omega}\otimes{\bf g}$, where ${\bf g}$ and…

We construct a natural conformally invariant one-form of weight $-2k$ on any $2k$-dimensional pseudo-Riemannian manifold which is closely related to the Pfaffian of the Weyl tensor. On oriented manifolds, we also construct natural…

Let $(M,g)$ be a Riemannian manifold, and $m$ be a second metric on $M$. We give expressions of $m$'s associated connection, and Riemann curvature tensor $R_m$, in terms of $R_g$ and certain combinations of covariant derivatives of $m$…

In this note, we evaluate the Weyl-invariant quadratic curvature tensors for the particular Weyl's gauge field constructed in the $3+1$-dimensional noncompact Weyl-Einstein-Yang-Mills model. We subsequently extend the model to its higher…

We give a necessary condition for a Riemannian manifold to admit limiting Carleman weights in terms of the Weyl tensor (in dimensions 4 and higher) and the Cotton-York tensor in dimension 3. As an application we provide explicit examples of…

The theory of spaces with different (not only by sign) contravariant and covariant affine connections and metrics [}$(\bar{L}_n,g)$\QTR{it}{-spaces] is worked out within the framework of the tensor analysis over differentiable manifolds and…

It is shown that in every dimension n=3j+2, j=1,2,3,..., there exist compact pseudo-Riemannian manifolds with parallel Weyl tensor, which are Ricci-recurrent, but neither conformally flat nor locally symmetric, and represent all indefinite…

We characterize manifolds which are locally conformally equivalent to either complex projective space or to its negative curvature dual in terms of their Weyl curvature tensor. As a byproduct of this investigation, we classify the…

Derdzinski and Shen's theorem on the restrictions posed by a Codazzi tensor on the Riemann tensor holds more generally when a Riemann-compatible tensor exists. Several properties are shown to remain valid in this broader setting. Riemann…

Free Lagrangians are found both for gauge and non-gauge bosonic conformal fields of any symmetry type and in any space-time dimension. Conformal gauge fields of various types, their gauge transformations and gauge invariant field strengths…

The problem of obtaining an explicit representation for the fourth invariant of geodesic motion (generalized Carter constant) of an arbitrary stationary axisymmetric vacuum spacetime generated from an Ernst Potential is considered. The…

A famous theorem of Weyl states that if $M$ is a compact submanifold of euclidean space, then the volumes of small tubes about $M$ are given by a polynomial in the radius $r$, with coefficients that are expressible as integrals of certain…

We apply the theory of Weyl structures for parabolic geometries developed by A. Cap and J. Slovak in to compute, for a quaternionic contact (qc) structure, the Weyl connection associated to a choice of scale, i.e. to a choice of…

The problem of characterizing conformally Einstein manifolds by tensorial conditions has been tackled recently in papers by M. Listing, and in work by A. R. Gover and P. Nurowski. Their results apply to metrics satisfying a "non-degeneracy"…

We write down the generalized Bessel function associated with the root system of type $D$ by means of multivariate hypergeometric series. Our hint comes from the particular case of the Brownian motion in the Weyl chamber of type $D$.

We investigate the coupling of matter to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form $L_m\tilde{R}^2$, where $L_m$ is the ordinary matter Lagrangian, and $\tilde{R}$ is the Weyl scalar. The coupling…

We present locally scale (Weyl) covariant generalisation of Minimal Massive Gravity theory using the language of exterior differential forms on Riemann-Cartan-Weyl space-times. The theory is expressed by a locally scale invariant action and…

We construct new families of conformally invariant differential operators acting on densities. We introduce a simple, direct approach which shows that all such operators arise via this construction when the degree is bounded by the…

We study Weyl conformal geometry as a general gauge theory of the Weyl group (of Poincar\'e and dilatations symmetries) in a manifestly Weyl gauge covariant formalism in which this geometry is automatically metric and physically relevant.…

General classical theories of material fields in an arbitrary Riemann-Cartan space are considered. For these theories, with the help of equations of balance, new non-trivially generalized, manifestly generally covariant expressions for…