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On local flatness of manifolds with AHS-structures

The AHS–structures on manifolds are the simplest cases of the so called parabolic geometries which are modeled on homogeneous spaces corresponding to a parabolic subgroup in a semisimple Lie group. It covers the cases where the negative parts of the graded Lie algebras in question are abelian. In the series [Čap, Slovák, Souček, 94, 95], the authors developed a consistent frame bundle approach to the subject. Here we give explicit descriptions of the obstructions against the flatness of such structures based on the latter approach. In particular we recover the results proved in [Baston] for complex manifolds in the real smooth setting.