Definite signature conformal holonomy: a complete classification

DOI10.1016/j.geomphys.2007.05.001zbMath1407.53050arXivmath/0503388OpenAlexW2023166767MaRDI QIDQ2456447

Stuart Armstrong

Publication date: 18 October 2007

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503388

zbMATH Keywords

coneholonomyEinstein manifoldconformal geometryCartan connectiontractor connection

Mathematics Subject Classification ID

Related Items (23)

Conformal holonomy, symmetric spaces, and skew symmetric torsion ⋮ Intrinsic holonomy and curved cosets of Cartan geometries ⋮ The ambient obstruction tensor and conformal holonomy ⋮ A holonomy characterisation of Fefferman spaces ⋮ Transitive conformal holonomy groups ⋮ Smooth metric measure spaces, quasi-Einstein metrics, and tractors ⋮ Conformal holonomy of \(\mathbb{C}\)-spaces, Ricci-flat, and Lorentzian manifolds ⋮ Holonomy reductions of Cartan geometries and curved orbit decompositions ⋮ Multiple almost Einstein structures with intersecting scale singularities ⋮ Ambient connections realising conformal tractor holonomy ⋮ Projective holonomy. I: Principles and properties ⋮ Conformal holonomy in MacDowell-Mansouri gravity ⋮ Projective holonomy II: Cones and complete classifications ⋮ A CLASS OF COMPACT POINCARÉ–EINSTEIN MANIFOLDS: PROPERTIES AND CONSTRUCTION ⋮ Einstein connections and involutions via parabolic geometries ⋮ The collapsing sphere product of Poincaré-Einstein spaces ⋮ Conformal holonomy of bi-invariant metrics ⋮ The zero set of a twistor spinor in any metric signature ⋮ Cones over pseudo-Riemannian manifolds and their holonomy ⋮ Aspects of conformal holonomy ⋮ A SUB-PRODUCT CONSTRUCTION OF POINCARÉ–EINSTEIN METRICS ⋮ Decomposable conformal holonomy in Riemannian signature ⋮ Reducible conformal holonomy in any metric signature and application to twistor spinors in low dimension

Cites Work

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• Projective holonomy II: Cones and complete classifications
• Ricci-corrected derivatives and invariant differential operators
• Obstructions to conformally Einstein metrics in \(n\) dimensions
• Tractor calculi for parabolic geometries
• Möbius structures and two dimensional EinsteinWeyl geometry
• Conformal Tensors. (Second Note.)
• The geometry of homogeneous submanifolds of hyperbolic space
• Conformal Einstein spaces in \(n\)-dimensions
• Invariant theory and calculus for conformal geometries

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