Non-regular |2|-graded geometries II: classifying geometries, and generic six-in-nine distributions

2009/02/06 by Stuart Armstrong, Armstrong, Stuart
Mathematics · #51F25 #53B05 #53B15 #53C15 #58A30 #58J60 #58J70 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Representation Theory (math.RT) #math.DG #math.RT #msc:51F25 #msc:53B05 #msc:53B15 #msc:53C15 #msc:58A30 #msc:58J60 #msc:58J70

paper · pdf · doi:10.48550/arxiv.0902.1136

arxiv created 2009/02/06 · openalex publication_date 2009/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Complementing the previous paper in the series, this paper classifies |2|-graded parabolic geometries, listing their important properties: the group G₀, the graded tangent bundle gr(T) and its algebraïc bracket, the relevant cohomology spaces and the standard Tractor bundle \mcT. Several of these geometries are then explored in more detail, and the paper ends with a case study that that partially solves the equivalence problem for generic six distributions on nine dimensional manifolds.

Citations

• Lie contact structures and chains

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