Related papers: Weyl structures for parabolic geometries

Hermitian bundle gerbes with connection are geometric objects for which a notion of surface holonomy can be defined for closed oriented surfaces. We systematically introduce bundle gerbes by closing the pre-stack of trivial bundle gerbes…

We give an elementary proof of the fact that any 4-dimensional para-Hermitian manifold admits a unique para-Kaehler--Weyl structure. We then use analytic continuation to pass from the para-complex to the complex setting and thereby show any…

A new method for the construction of conformally invariant equations in an arbitrary four dimensional (pseudo-) Riemannian space is presented. This method uses the Weyl geometry as a tool and exploits the natural conformal invariance we can…

Complete complex parabolic geometries (including projective connections and conformal connections) are flat and homogeneous. This is the first global theorem on parabolic geometries.

We classify the possible local holonomy groups of Weyl connections. The Berger-Simons theorem and the Merkulov-Schwachh\"ofer classification of holonomy groups of irreducible torsion-free connections leaves us with the remaining case, where…

The chains studied in this paper generalize Chern-Moser chains for CR structures. They form a distinguished family of one dimensional submanifolds in manifolds endowed with a parabolic contact structure. Both the parabolic contact structure…

BGG resolutions and generalized BGG resolutions from representation theory of semisimple Lie algebras have been generalized to sequences of invariant differential operators on manifolds endowed with a geometric structure belonging to the…

Let $G$ be a simple algebraic group of type $E_6$ over an algebraically closed field of characteristic $p>0$. We determine the submodule structure of the Weyl modul es with highest weight $r\omega_1$ for $0\leq r\leq p-1$, where $\omega_1$…

Using a combination of techniques from conformal and complex geometry, we show the potentialization of 4-dimensional closed Einstein-Weyl structures which are half-algebraically special and admit a "half-integrable" almost-complex…

We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser {\it et al.}, and S. Majid. For any finite Weyl group $W$ we consider the subalgebra generated by flat…

On a (pseudo-) Riemannian manifold of dimension n > 2, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives…

In this article, we study the gauge theoretic aspects of real and quaternionic parabolic bundles over a real curve $(X, \sigma_X)$, where X is a compact Riemann surface and {\sigma}X is an anti-holomorphic involution. For a fixed real or…

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 consider compact conformal manifolds $(M,[g])$ endowed with a closed Weyl structure $\nabla$, i.e. a torsion-free connection preserving the conformal structure, which is locally but not globally the Levi-Civita connection of a metric in…

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 establish a one-to-one correspondence between K\"ahler metrics in a given conformal class and parallel sections of a certain vector bundle with conformally invariant connection, where the parallel sections satisfy a set of non--linear…

This paper introduces and studies a class of Weyl-type algebras \(A_{p,t,\cA} = \Weyl{e^{\pm x^{p} e^{t x}},\; e^{\cA x},\; x^{\cA}}\) constructed over exponential-polynomial rings, where \(\FF\) is a field of characteristic zero, \(\cA\)…

The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry -…

For a torsionless connection on the tangent bundle of a manifold M the Weyl curvature W is the part of the curvature in kernel of the Ricci contraction. We give a coordinate free proof of Weyl's result that the Weyl curvature vanishes if…

In this paper, we study the moduli spaces of parabolic connections with a quadratic differential. We endow these moduli spaces with symplectic structures by using the fundamental 2-forms on the moduli spaces of parabolic connections (which…