We prove that if is a complete simply connected Riemannian manifold and is a totally geodesic foliation of with integrable normal bundle, then 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 est une variété riemannienne complète simplement connexe et est un feuilletage totalement géodésique sur dont le fibré orthogonal est involutif, alors 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}, pages = {183--198}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {33}, number = {2}, year = {1983}, doi = {10.5802/aif.923}, zbl = {0487.57010}, mrnumber = {84j:53042}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.923/} }
TY - JOUR AU - Blumenthal, Robert A. AU - Hebda, James J. TI - De Rham decomposition theorems for foliated manifolds JO - Annales de l'Institut Fourier PY - 1983 SP - 183 EP - 198 VL - 33 IS - 2 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.923/ DO - 10.5802/aif.923 LA - en ID - AIF_1983__33_2_183_0 ER -
%0 Journal Article %A Blumenthal, Robert A. %A Hebda, James J. %T De Rham decomposition theorems for foliated manifolds %J Annales de l'Institut Fourier %D 1983 %P 183-198 %V 33 %N 2 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.923/ %R 10.5802/aif.923 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.923/
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