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Parabolic Geometries I
The first monograph on parabolic geometry in the literature following several ground-braking results achieved by the authors and their collaborators in the last two decades. The volume will beExpand
Bernstein-Gelfand-Gelfand sequences
The Bernstein-Gelfand-Gelfand sequences extend the complexes of homogeneous vector bundles to curved Cartan geometries.
Infinitesimal automorphisms and deformations of parabolic geometries
We show that infinitesimal automorphisms and infinitesimal deformations of parabolic geometries can be nicely described in terms of the twisted de--Rham sequence associated to a certain linearExpand
On twisted tensor products of algebras
(1995). On twisted tensor products of algebras. Communications in Algebra: Vol. 23, No. 12, pp. 4701-4735.
Parabolic geometries and canonical Cartan connections
Let G be a (real or complex) semisimple Lie group, whose Lie algebra g is endowed with a so called |k|–grading, i.e. a grading of the form g = g−k ⊕ · · · ⊕ gk, such that no simple factor of G is ofExpand
Weyl structures for parabolic geometries
Motivated by the rich geometry of conformal Riemannian manifolds and by the recent development of geometries modeled on homogeneous spaces $G/P$ with $G$ semisimple and $P$ parabolic, Weyl structuresExpand
Correspondence spaces and twistor spaces for parabolic geometries
Abstract For a semisimple Lie group G with parabolic subgroups Q ⊂ P ⊂ G, we associate to a parabolic geometry of type (G, P) on a smooth manifold N the correspondence space ℭ N, which is the totalExpand
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
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
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
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