Free 3-distributions: holonomy, Fefferman constructions and dual distributions

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 $G_2^{\prime }$. The paper concludes with some holonomy constructions for free $n$-distributions for $n>3$.

a corrected and improved version, 24 pages

References in corpus (1)

• Generalised Einstein condition and cone construction for parabolic geometries

Cited by in corpus (1)

• Inclusions between parabolic geometries