Subcomplexes in Curved BGG-Sequences

Details Subcomplexes in Curved BGG-Sequences Subcomplexes in Curved BGG-Sequences

2005-08-26

arxiv.org/abs/math/0508534v1

Mathematics

Differential Geometry

29 pages, no figures

Scientific paper

BGG-sequences offer a uniform construction for invariant differential operators for a large class of geometric structures called parabolic geometries. For locally flat geometries, the resulting sequences are complexes, but in general the compositions of the operators in such a sequence are nonzero. In this paper, we show that under appropriate torsion freeness and/or semi-flatness assumptions certain parts of all BGG sequences are complexes. Several examples of structures, including quaternionic structures, hypersurface type CR structures and quaternionic contact structures are discussed in detail. In the case of quaternionic structures we show that several families of complexes obtained in this way are elliptic.

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