De Rham decomposition theorems for foliated manifolds
Annales de l'Institut Fourier, Volume 33 (1983) no. 2, p. 183-198

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.

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.

@article{AIF_1983__33_2_183_0,
     author = {Blumenthal, Robert A. and Hebda, James J.},
     title = {De Rham decomposition theorems for foliated manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {33},
     number = {2},
     year = {1983},
     pages = {183-198},
     doi = {10.5802/aif.923},
     zbl = {0487.57010},
     mrnumber = {84j:53042},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1983__33_2_183_0}
}
Blumenthal, Robert A.; Hebda, James J. De Rham decomposition theorems for foliated manifolds. Annales de l'Institut Fourier, Volume 33 (1983) no. 2, pp. 183-198. doi : 10.5802/aif.923. http://www.numdam.org/item/AIF_1983__33_2_183_0/

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