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Projective holonomy I: principles and properties

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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.

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  1. Mathematics Department, Oxford University, Oxford, OX1 3LB, UK

    Stuart Armstrong

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  1. Stuart Armstrong
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Armstrong, S. Projective holonomy I: principles and properties. Ann Glob Anal Geom 33, 47–69 (2008). https://doi.org/10.1007/s10455-007-9076-6

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