相关论文: Ambient connections realising conformal Tractor ho…

We examine questions of geometric realizability for algebraic structures which arise naturally in affine and Riemannian geometry. Suppose given an algebraic curvature operator R at a point P of a manifold M and suppose given a real analytic…

The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…

Here we treat the problem: given a torsion-free connection do its geodesics, as unparametrised curves, coincide with the geodesics of an Einstein metric? We find projective invariants such that the vanishing of these is necessary for the…

Pre-geodesics of an affine connection are the curves that are geodesics after a reparametrization (the analogous concept in K\"ahler geometry is known as J-planar curves). Similarly, dual-geodesics on a Riemannian manifold are curves along…

We show that if a Finsler space is conformally automorphic to a Riemannian space and the automorphism is positively homogeneous with respect to tangent vectors, then the indicatrix of the Finsler space is a space of constant curvature. In…

Let $\mathbf{g}$ be a pseudo--Riemanian metric of arbitrary signature on a manifold $\mathbf{V}$ with conventional $n+n$ dimensional splitting, $\ n\geq 2,$ determined by a nonholonomic (non--integrable) distribution $\mathcal{N}$ defining…

We develop the natural tractor calculi associated to conformal and CR structures as a fundamental tool for the study of Fefferman's construction of a canonical conformal class on the total space of a circle bundle over a non--degenerate CR…

The polynomial affine gravity is a model that is built up without the explicit use of a metric tensor field. In this article we reformulate the three-dimensional model and, given the decomposition of the affine connection, we analyse the…

We prove the existence and uniqueness of a weighted analogue of the Fefferman-Graham ambient metric for manifolds with density. We then show that this ambient metric forms the natural geometric framework for the singular Ricci flow: given a…

Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…

We show that given a conformal structure whose holonomy representation fixes a totally lightlike subspace of arbitrary dimension, there is always a local metric in the conformal class off a singular set which is Ricci-isotropic and gives…

The usual ambient space approach to conformal fields is based on identifying the d-dimensional conformal space as the Dirac projective hypercone in a flat d+2-dimensional ambient space. In this work, we explicitly concentrate on singletons…

We define a conformal reference frame, i.e., a special projection of the six-dimensional sky bundle of a Lorentzian manifold (or the five-dimensional twistor space) to a three-dimensional manifold. We construct an example, a conformal…

We show how an affine connection on a Riemannian manifold occurs naturally as a cochain in the complex for Leibniz cohomology of vector fields with coefficients in the adjoint representation. The Leibniz coboundary of the Levi-Civita…

This paper is a review of the twistor theory of irreducible G-structures and affine connections. Long ago, Berger presented a very restricted list of possible irreducibly acting holonomies of torsion-free affine connections. His list was…

We state and prove a simple Theorem that allows one to generate invariant quantities in Metric-Affine Geometry, under a given transformation of the affine connection. We start by a general functional of the metric and the connection and…

The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for…

A Riemann-Cartan manifold is a Riemannian manifold endowed with an affine connection which is compatible with the metric tensor. This affine connection is not necessarily torsion free. Under the assumption that the manifold is a homogeneous…

Recent proposals for a nontrivial quantization of covariant, nonrenormalizable, self-interacting, scalar quantum fields have emphasized the importance of quantum fields that obey affine commutation relations rather than canonical…

We consider a 3-dimensional Riemannian manifold V with a metric g and an affinor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we…