De Rham decomposition theorems for foliated manifolds

Blumenthal, Robert A.; Hebda, James J.

Annales de l'Institut Fourier, Tome 33 (1983) no. 2, pp. 183-198.

Nous démontrons que si $M$ est une variété riemannienne complète simplement connexe et $F$ est un feuilletage totalement géodésique sur $M$ dont le fibré orthogonal est involutif, alors $M$ est topologiquement un produit et les deux feuilletages sont les feuilletages produits. Nous démontrons aussi un théorème de décomposition pour les feuilletages riemanniens et un théorème de structure pour les feuilletages riemanniens à courbure récurrente.

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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