Stuart Armstrong
Projective Holonomy I: Principles and Properties
Preprint series: ESI preprints

MSC:

53B10 Projective connections

Abstract: The aim of this paper and its sequel is to introduce and classify the holonomy
algebras of the projective Tractor connection. After a brief historical background,
this paper presents and analyses the projective Cartan and Tractor connections, the
various structures they can preserve, and their geometric interpretations. Preserved
subbundles of the Tractor bundle generate foliations with Ricci-flat leaves. Contact-
and Einstein-structures arise from other reductions of the Tractor holonomy, as do
$U(1)$ and $Sp(1, \mathbb{H})$ bundles over a manifold of smaller dimension.


Keywords: holonomy, Cartan connection, tractor connection, projective structures, projective connections, cones, contact, quaternionic, complex projective, Ricci-flat, Einstein, torsion-free