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Annals of Global Analysis and Geometry

, Volume 33, Issue 2, pp 137–160 | Cite as

Projective holonomy II: cones and complete classifications

  • Stuart ArmstrongEmail author
Original Paper

Abstract

The aim of this paper and its prequel is to introduce and classify the irreducible holonomy algebras of the projective Tractor connection. This is achieved through the construction of a ‘projective cone’, a Ricci-flat manifold one dimension higher whose affine holonomy is equal to the Tractor holonomy of the underlying manifold. This paper uses the result to enable the construction of manifolds with each possible holonomy algebra.

Keywords

Holonomy Projective structures Tractor connections Cones Cartan connections 

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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of MathematicsOxford UniversityOxfordUK

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