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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. Blumenthal; James 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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