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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 be… Expand

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

- A. Čap
- Mathematics
- 26 August 2005

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 linear… Expand

On twisted tensor products of algebras

- A. Čap, H. Schichl, J. Vancura
- Mathematics
- 1995

(1995). On twisted tensor products of algebras. Communications in Algebra: Vol. 23, No. 12, pp. 4701-4735.

Parabolic geometries and canonical Cartan connections

- A. Čap, H. Schichl
- Mathematics
- 1 February 2000

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 of… Expand

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 structures… Expand

Correspondence spaces and twistor spaces for parabolic geometries

- A. Čap
- Mathematics
- 13 February 2001

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 total… Expand

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 are… Expand

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 ambient… Expand

Holonomy reductions of Cartan geometries and curved orbit decompositions

- A. Čap, A. Gover, M. Hammerl
- Mathematics
- 23 March 2011

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 initial… Expand

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