arXiv research

Study Weyl-Einstein structures on conformal solvmanifolds, proving Einstein property and classifying metrics.

Study properties of Kenmotsu manifolds with conformal η-Einstein soliton metrics.

Einstein metrics on products are shown to be warped.

Global obstructions found for conformally Einstein metrics in 6D.

Study properties of para-Kähler manifolds with conformal Einstein soliton metrics.

In this paper we first use the result in $[12]$ to remove the assumption of the $L^2$ boundedness of Weyl curvature in the gap theorem in $[9]$ and then obtain a gap theorem for a class of conformally compact Einstein manifolds with very large renormalized volume. We also uses the blow-up method to derive curvature est…

The study characterizes and classifies specific types of manifolds using conformal and quasi-Einstein properties.

Study on 4D Einstein manifolds with Kähler conformal geometry.

New conformally Einstein metrics on Heisenberg group found.

A Riemannian or pseudo-Riemannian (or conformal) structure is conformally Einstein if and only if there is a suitably generic parallel section of a certain vector bundle -- the so-called standard conformal tractor bundle. We show that this characterisation leads to a systematic approach to constructing obstructions to …

Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably related, we give an explicit construction of a Poincaré-Einstein (pseudo-)metric with conformal infinity the conformal class of the product of the initial metrics. We show that these metrics are equivalent to ambient metrics for the given conforma…

In this paper we study the topology of conformally compact Einstein 4-manifolds. When the conformal infinity has positive Yamabe invariant and the renormalized volume is also positive we show that the conformally compact Einstein 4-manifold will have at most finite fundamental group. Under the further assumption that t…

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products of Kahler-Einstein manifolds. We compute the associated conformal invariants, i…

New proof of instability for certain Einstein metrics.

The article defines conditions for a manifold to be conformal to an Einstein space.

The paper studies special solitons on specific contact metric manifolds.

New tensors help determine if metrics are related to Poincaré-Einstein ones.

The paper explores rigidity in conformal submersions and quasi-Einstein manifolds.

New examples of weakly Einstein conformal products are constructed.

Symmetries of Einstein-Weyl manifolds can be extended from boundary surfaces.

The study proves rigidity for Poincaré-Einstein manifolds with flat Euclidean conformal infinity.

Study on filling 3D metrics with 4D Poincaré-Einstein structures.

A new definition of canonical conformal differential operators $P_k$ ($k=1,2,...)$, with leading term a $k^{\rm th}$ power of the Laplacian, is given for conformally Einstein manifolds of any signature. These act between density bundles and, more generally, between weighted tractor bundles of any rank. By construction …

15 Einstein 4-manifolds with positive conformal curvature are classified.

An indecomposable Lie group with Riemannian bi-invariant metric is always simple and hence Einstein. For indefinite metrics this is no longer true, not even for simple Lie groups. We study the question of whether a semi-Riemannian bi-invariant metric is conformal to an Einstein metric. We obtain results for all three c…

New $\mathcal{C}$-connection characterizes 4D spaces conformal to Einstein spaces.

We find a new obstruction for a real Einstein 4-orbifold with an A1-singularity to be a limit of smooth Einstein 4-manifolds. The obstruction is a curvature condition at the singular point. For asymptotically hyperbolic metrics, with boundary at infinity a conformal metric, we prove that if the obstruction vanishes, on…

Paper proves uniqueness of Einstein metrics on balls.

A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the presence of matter it is possible to construct a conformal gauge which allows to kno…

On a conformal manifold, it is well known that parallel sections of the standard tractor bundle with non-vanishing scale are in 1-1 correspondence with solutions of the conformal Einstein equation. In 2 dimensions conformal geometry carries no local information but one can remedy this by equipping the surface with a Mö…

Develops methods for computing conformal invariants of submanifolds.

An almost Einstein manifold satisfies equations which are a slight weakening of the Einstein equations; Einstein metrics, Poincare-Einstein metrics, and compactifications of certain Ricci-flat asymptotically locally Euclidean structures are special cases. The governing equation is a conformally invariant overdetermined…

We simplify and extend a 6D conformal gravity theory to 8D, linking it to Q-curvature.

A conformal description of Poincare-Einstein manifolds is developed: these structures are seen to be a special case of a natural weakening of the Einstein condition termed an almost Einstein structure. This is used for two purposes: to shed light on the relationship between the scattering construction of Graham-Zworski…

This article describes some geometric invariants and conformal anomalies for conformally compact Einstein manifolds and their minimal submanifolds which have recently been discovered via the Anti-de Sitter/Conformal Field Theory correspondence.

We study the affine quasi-Einstein Equation for homogeneous surfaces. This gives rise through the modified Riemannian extension to new half conformally flat generalized quasi-Einstein neutral signature $(2,2)$ manifolds, to conformally Einstein manifolds and also to new Einstein manifolds through a warped product const…

Classifies smooth metric measure spaces with two weighted Einstein representatives.

Researchers create compatibility complexes for Einstein metrics.

The paper explores p-biharmonic hypersurfaces in Einstein and conformally flat spaces.

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" condition on the Weyl tensor \W. We investigate the geometry of the foliations …

New conformal geometry method solves Einstein-Weyl equations.

Weyl derivatives, Weyl-Lie derivatives and conformal submersions are defined, then used to generalize the Jones-Tod correspondence between selfdual 4-manifolds with symmetry and Einstein-Weyl 3-manifolds with an abelian monopole. In this generalization, the conformal symmetry is replaced by a particular kind of conform…

We propose further conformal parametrizations for initial data in some modified Einstein gravity theories. Some of them give rise to conformally covariant systems.

We show that locally conformally flat quasi-Einstein manifolds are globally conformally equivalent to a space form or locally isometric to a $pp$-wave or a warped product.

Compact formulas for Yang-Mills conditions on conformal manifolds.

We analyze the classic problem of existence of Einstein metrics in a given conformal structure for the class of conformal structures inducedf Nurowski's construction by (oriented) (2,3,5) distributions. We characterize in two ways such conformal structures that admit an almost Einstein scale: First, they are precisely …

We compute renormalized curvature integrals on Poincaré-Einstein manifolds.

We give a classification of compact conformally Kahler Einstein-Weyl manifolds whose Ricci tensor is hermitian.