Related papers: Explicit ambient metrics and holonomy

This paper aims to classify the holonomy of the conformal Tractor connection, and relate these holonomies to the geometry of the underlying manifold. The conformally Einstein case is dealt with through the construction of metric cones,…

The hierarchy of conformally invariant k-th powers of the Laplacian acting on a scalar field with scaling dimensions $\Delta_{(k)}=k-d/2$, k=1,2,3 as obtained in the recent work [1] is rederived using the Fefferman-Graham d+2 dimensional…

A locally conformally K\"ahler (lcK) manifold is a complex manifold $(M,J)$ together with a Hermitian metric $g$ which is conformal to a K\"ahler metric in the neighbourhood of each point. In this paper we obtain three classification…

We demonstrate that all perturbative scale invariant heterotic sigma models with a compact target space $M^D$ are conformally invariant. The proof, presented in detail for up to and including two loops, utilises a geometric analogue of the…

Harmonic coordinate conditions in stationary asymptotically flat spacetimes with matter sources have more than one solution. The solutions depend on the degree of smoothness of the metric and its first derivatives, which we wish to impose…

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 study the moduli space of coherent systems in $P^2$ using the Segre invariant. We obtain necessary conditions for the existence of $\alpha$-semistable coherent systems $(E,V)$ of type $(2, c_1, c_2, k)$, with $k \geq 2$. Afterwards, we…

We characterize the representations of the fundamental group of a closed surface to $\mathrm{PSL}_2(\mathbb C)$ that arise as the holonomy of a branched complex projective structure with fixed branch divisor. In particular, we compute the…

In this paper we relate the Fefferman-Graham ambient metric construction for conformal manifolds to the approach to conformal geometry via the canonical Cartan connection. We show that from any ambient metric that satisfies a weakening of…

All hypersurface homogeneous locally rotationally symmetric spacetimes which admit conformal symmetries are determined and the symmetry vectors are given explicitly. It is shown that these spacetimes must be considered in two sets. One set…

The holonomy algebras of Einstein not Ricci-flat pseudo-Riemannian manifolds of arbitrary signature are classified. As illustrating examples, the cases of Lorentzian manifolds, pseudo-Riemannian manifolds of signature $(2,n)$ and the…

We introduce a class of maps from an affine flat into a Riemannian manifold that solve an elliptic system defined by the natural second order elliptic operator of the affine structure and the nonlinear Riemann geometry of the target. These…

Irreducible sigma models, i.e. those for which the partition function does not factorise, are defined on Riemannian spaces with irreducible holonomy groups. These special geometries are characterised by the existence of covariantly constant…

We study explicit conformal minimal immersions into $\mathbb{R}^5$ obtained from holomorphic null curves in $\mathbb{C}^5$. Although the general correspondence between conformal minimal immersions in $\mathbb{R}^n$ and holomorphic null data…

We give a classification of non-Abelian T-duals of the flat metric in D=4 dimensions with respect to the four-dimensional continuous subgroups of the Poincare group. After dualizing the flat background, we identify majority of dual models…

We show that C^2 conformally compact Riemannian Einstein metrics have conformal compactifications that are smooth up to the boundary in dimension 3 and all even dimensions, and polyhomogeneous in odd dimensions greater than 3.

The necessary and sufficient conditions for a three-dimensional Riemannian metric to admit a transitive group of isometries are obtained. These conditions are Intrinsic, Deductive, Explicit and ALgorithmic, and they offer an IDEAL labeling…

This paper provides details of the construction, properties and some applications of the ambient metric associated to a conformal class of metrics on a smooth manifold. Existence and uniqueness of formal expansions defining such metrics are…

Presented are exactly integrable models with pure radiation in R^2 gravity with a cosmological constant, related to wave-like Shapovalov spacetimes type II. Spatially homogeneous models of Shapovalov spaces were considered. The obtained…

By replacing the internal energy with the free energy, as coordinates in a "space of observables", we slightly modify (the known three) non-holonomic geometrizations and show that the coefficients of the curvature tensor field, of the Ricci…