Projective Geometry II: Cones and Complete Classifications
Stuart Armstrong

TL;DR
This paper classifies irreducible holonomy algebras of the projective Tractor connection by constructing Ricci-flat cones, enabling the creation of manifolds with all possible holonomy algebras.
Contribution
It introduces a novel approach using projective cones to classify and construct manifolds with specific holonomy algebras, extending previous work.
Findings
Constructed Ricci-flat cones corresponding to Tractor holonomies
Achieved classification of irreducible holonomy algebras
Enabled explicit manifold constructions for each holonomy
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.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds
