Open AccessPosted Content
Free 3-distributions: holonomy, Fefferman constructions and dual distributions
Reads0
Chats0
TLDR
In this article, the authors analyzed the parabolic geometries generated by a free 3-distribution in the tangent space of a manifold and showed the existence of normal Fefferman constructions over CR and Lagrangian contact structures corresponding to holonomy reductions to SO(4,2) and SO(3,3), respectively.Abstract:
This paper analyses the parabolic geometries generated by a free 3-distribution in the tangent space of a manifold. It shows the existence of normal Fefferman constructions over CR and Lagrangian contact structures corresponding to holonomy reductions to SO(4,2) and SO(3,3), respectively. There is also a fascinating construction of a `dual' distribution when the holonomy reduces to $G_2'$. The paper concludes with some holonomy constructions for free $n$-distributions for $n>3$.read more
Citations
More filters
Journal ArticleDOI
The twistor spinors of generic 2- and 3-distributions
TL;DR: In this paper, the conformal spin geometries are characterized by their conformal holonomy and equivalently by the existence of a twistor spinor which satisfies a genericity condition.
DissertationDOI
Applications of Cartan and tractor calculus to conformal and CR-geometry
TL;DR: The main object of the Habilitationsschrift is the geometric study of solutions of overdetermined conformally invariant differential equations via the use of Cartan and tractor calculus as discussed by the authors.
Journal ArticleDOI
The twistor spinors of generic 2- and 3-distributions
TL;DR: In this paper, the conformal spin geometries are characterized by their conformal holonomy and equivalently by the existence of a twistor spinor which satisfies a genericity condition.
Weyl structures for generic rank two distributions in dimension five
TL;DR: In this paper, a dissertation about the untersuchung of Distributionen is presented, which is based on the Theorie der Weylstrukturen and parabolische geometrien.
Posted Content
Note on pre-Courant algebroid structures for parabolic geometries
TL;DR: In this article, it was shown that every parabolic geometry has a naturally defined per-Courant algebraic structure, which is called Courant algebras, if and only if the curvature of the Cartan connection vanishes.
References
More filters
Book ChapterDOI
Lie Algebra Cohomology and the Generalized Borel-Weil Theorem
TL;DR: The present paper will be referred to as Part I. A subsequent paper entitled, "Lie algebra cohomology and generalized Schubert cells, this article, which is referred as Part II.
Journal ArticleDOI
Metrics with exceptional holonomy
TL;DR: In this paper, it was shown that there exist metrics with holonomy G2 and Spin(7) and that the Cartan-Kahler theorem can be used to prove the existence of solutions whose holonomy is G2 or Spin(6).
Book
The Penrose Transform: Its Interaction with Representation Theory
TL;DR: A brief review of representation theory homogeneous bundles on G/P is given in this article with a remark on inverse images and a prototype translating BGG resolutions for G/B in the general case.
Journal ArticleDOI
Parabolic geometries and canonical Cartan connections
Andreas Cap,Hermann Schichl +1 more
TL;DR: In this article, the geometrical meaning of Cartan connections corresponding to the pair (G,P ) and the basic properties of these geometric connections are studied. But the authors focus on the Cartan connection in the context of Lie groups.
Journal ArticleDOI
Tractor calculi for parabolic geometries
Andreas Cap,A. R. Gover +1 more
TL;DR: In this paper, a tractors with canonical linear connections for all parabolic geometries are presented, which are analogous to a covariant derivative, iterable and defined on all vector bundles on parabolic geometry.