On uniqueness of submaximally symmetric parabolic geometries

2021/07/22 by The, Dennis
#17B70 #22E46 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 58J70 #Secondary 53B99

paper · doi:10.48550/arxiv.2107.10500

Abstract

Among (regular, normal) parabolic geometries of type (G,P), there is a locally unique maximally symmetric structure and it has symmetry dimension dim(G). The symmetry gap problem concerns the determination of the next realizable (submaximal) symmetry dimension. When G is a complex or split-real simple Lie group of rank at least three or when (G,P) = (G₂,P₂), we establish a local uniqueness result for submaximally symmetric structures of type (G,P).

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