Automorphism Groups of Parabolic Geometries

On Automorphism Groups of Parabolic Geometries

Partial linear spaces built on hexagons

We define four families of geometries with as point graph the graph — or its complement — of all elliptic 4 hyperplanes of a given parabolic quadric in any finite 6-dimensional projective space, where adjacency is 5 given by intersecting in a tangent 4-space. One of the classes consists of semi-partial geometries constructed 6 in J.A. Thas [SPG-reguli and semipartial geometries, Adv. Geom. 1 (2...

On Automorphism Groups of Some Types of Generic Distributions

To certain types of generic distributions (subbundles in a tangent bundle) one can associate canonical Cartan connections. Many of these constructions fall into the class of parabolic geometries. The aim of this article is to show how strong restrictions on the possibles sizes of automorphism groups of such distributions can be deduced from the existence of canonical Cartan connections. This ne...

Essential Parabolic Structures and Their Infinitesimal Automorphisms

Using the theory of Weyl structures, we give a natural generalization of the notion of essential conformal structures and conformal Killing fields to arbitrary parabolic geometries. We show that a parabolic structure is inessential whenever the automorphism group acts properly on the base space. As a corollary of the generalized Ferrand–Obata theorem proved by C. Frances, this proves a generali...

On the Geometry of Chains

The chains studied in this paper generalize Chern–Moser chains for CR structures. They form a distinguished family of one dimensional submanifolds in manifolds endowed with a parabolic contact structure. Both the parabolic contact structure and the system of chains can be equivalently encoded as Cartan geometries (of different types). The aim of this paper is to study the relation between these...