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

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

2009-02-06

arxiv.org/abs/0902.1136v1

Mathematics

Differential Geometry

Scientific paper

Complementing the previous paper in the series, this paper classifies $|2|$-graded parabolic geometries, listing their important properties: the group $G_0$, the graded tangent bundle $gr(T)$ and its algebra\"ic bracket, the relevant cohomology spaces and the standard Tractor bundle $\mc{T}$. 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.

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