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Projective Geometry II: Cones and Complete Classifications

Research paper by Stuart Armstrong

Indexed on: 13 Mar '07Published on: 13 Mar '07Published in: Mathematics - Differential Geometry



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.