English

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

Differential Geometry 2009-02-09 v1 Representation Theory

Abstract

Complementing the previous paper in the series, this paper classifies 2|2|-graded parabolic geometries, listing their important properties: the group G0G_0, the graded tangent bundle gr(T)gr(T) and its algebra\"ic bracket, the relevant cohomology spaces and the standard Tractor bundle \mcT\mc{T}. 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.

Keywords

Cite

@article{arxiv.0902.1136,
  title  = {Non-regular $|2|$-graded geometries II: classifying geometries, and generic six-in-nine distributions},
  author = {Stuart Armstrong},
  journal= {arXiv preprint arXiv:0902.1136},
  year   = {2009}
}