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arXiv 0902.1136math.DGmath.RT
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非规则$|2|$ -分级几何II:几何分类和一般六进九分布

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

Stuart Armstrong

摘要:

本文对$|2|$ -分次抛物几何进行了分类,给出了它们的重要性质:$G_0$群,分次切丛$gr(T)$及其代数括号,相应的上同调空间和标准Tractor丛$\mc{T}$ .其中几个几何形状,然后更详细地探讨,并结束了一个案例研究,部分解决了九维流形上的通用六分布的等价性问题。

英文摘要:

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 algebraïc 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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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