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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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