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Transversely homogeneous foliations

Robert A. Blumenthal — 1979

Annales de l'institut Fourier

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 case,...

De Rham decomposition theorems for foliated manifolds

Robert A. BlumenthalJames J. Hebda — 1983

Annales de l'institut Fourier

We prove that if M is a complete simply connected Riemannian manifold and F is a totally geodesic foliation of M with integrable normal bundle, then M is topologically a product and the two foliations are the product foliations. We also prove a decomposition theorem for Riemannian foliations and a structure theorem for Riemannian foliations with recurrent curvature.

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