Non-regular $|2|$-graded geometries I: general theory - Mathematics > Differential GeometryReport as inadecuate




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Abstract: This paper analyses non-regular $|2|$-graded geometries, and show that theyshare many of the properties of regular geometries - the existence of a uniquenormal Cartan connection encoding the structure, the harmonic curvature asobstruction to flatness of the geometry, the existence of the first two BGGsplitting operators and of in most cases invariant prolongations for thestandard Tractor bundle $\mc{T}$. Finally, it investigates whether thesegeometries are determined entirely by the distribution $H = T {-1}$ andconcludes that this is generically the case, up to a finite choice, whenever$H^1\mf{g}^1,\mf{g}$ vanishes in non-negative homogeneity.



Author: Stuart Armstrong

Source: https://arxiv.org/







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