Measure preserving pseudo-groups and a theorem of Sacksteder

Joseph F. Plante

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Transversely homogeneous foliations

Robert A. Blumenthal (1979)

Annales de l'institut Fourier

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A foliation of a manifold is transversely homogeneous if it can be defined by local submersions to a homogeneous space $G / K$ which on overlaps differ by translations. We explore the topology and geometry of such foliations and give a structure theorem for the case when $K$ is compact. We investigate the relationship between the structure equations of $G$ and the normal bundle of the foliation and provide a differential forms characterization of a large class of homogeneous foliations. As a special...