Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds - Characterization and Killing-Field Decomposition

2009/08/04 by Matthias Hammerl, Katja Sagerschnig · 3 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.3842/sigma.2009.081

published as SIGMA 5 (2009), 081, 29 pages · Misprints in Theorem B are corrected

openalex publication_date 2009/08/04 · arxiv created 2009/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a maximally non-integrable 2-distribution D on a 5-manifold M , it was discovered by P. Nurowski that one can naturally associate a conformal structure [g] D of signature (2, 3) on M . We show that those conformal structures [g] D which come about by this construction are characterized by the existence of a normal conformal Killing 2-form which is locally decomposable and satisfies a genericity condition. We further show that every conformal Killing field of [g] D can be decomposed into a symmetry of D and an almost Einstein scale of [g] D .

Citations

• A remark on conformal \SU(p,q)-holonomy
• Invariant Prolongation of BGG-Operators in Conformal Geometry
• Almost Einstein and Poincare-Einstein manifolds in Riemannian signature

Cited by

• The twistor spinors of generic 2- and 3-distributions
• On the eta invariant of (2,3,5) distributions
• The Heat Asymptotics on Filtered Manifolds

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• The twistor spinors of generic 2- and 3-distributions
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• Local equivalence of some maximally symmetric rolling distributions and SU(2) Pfaffian systems