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CR invariant powers of the sub-Laplacian
Abstract CR invariant differential operators on densities with leading part a power of the sub-Laplacian are derived. One family of such operators is constructed from the ‘‘conformally invariantExpand
Conformally invariant powers of the Laplacian — A complete nonexistence theorem
Conformally invariant operators and the equations they determine play a central role in the study of manifolds with pseudo-Riemannian, Riemannian, conformai and related structures. This observationExpand
Conformally invariant non-local operators
On a conformal manifold with boundary, we construct conformally invariant local boundary conditions B for the conformally invariant power of the Laplacian k , with the property that ( k , B) isExpand
Tractor calculi for parabolic geometries
Parabolic geometries may be considered as curved analogues of the homogeneous spaces G/P where G is a semisimple Lie group and P C G a parabolic subgroup. Conformal geometries and CR geometries areExpand
Conformally Invariant Powers of the Laplacian, Q-Curvature, and Tractor Calculus
Abstract: We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differentialExpand
Standard Tractors and the Conformal Ambient Metric Construction
In this paper we relate the Fefferman–Graham ambientmetric construction for conformal manifolds to the approach toconformal geometry via the canonical Cartan connection. We show thatfrom any ambientExpand
Almost Einstein and Poincare-Einstein manifolds in Riemannian signature
  • A. Gover
  • Mathematics, Physics
  • 25 March 2008
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-flatExpand
Obstructions to conformally Einstein metrics in n dimensions
Abstract We construct polynomial conformal invariants, the vanishing of which is necessary and sufficient for an n-dimensional suitably generic (pseudo-)Riemannian manifold to be conformal to anExpand
Holonomy reductions of Cartan geometries and curved orbit decompositions
We develop a holonomy reduction procedure for general Cartan geometries. We show that, given a reduction of holonomy, the underlying manifold naturally decomposes into a disjoint union of initialExpand