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A topological obstruction for a foliation be a sub-foliation of another is given by comparing the images of the associated characteristic homomorphisms (in the sense of Lehmann).
The homogeneous quaternionic Kähler structures on the Alekseevskian 𝒲-spaces with their natural quaternionic structures, each of these spaces described as a solvable Lie group, and the type of such structures in Fino's classification, are found.
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