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Pseudogroupes d’holonomie des feuilletages riemanniens sur des variétés compactes 1-connexes. (Holonomy pseudogroups of Riemannian foliations on compact 1-connected manifolds). (French) Zbl 0647.57019
Géométrie différentielle, Colloq. Géom. Phys., Paris/Fr. 1986, Trav. Cours 33, 141-160 (1988).
[For the entire collection see Zbl 0635.00010.]
The paper contains the classification of holonomy pseudogroups of Riemannian foliations on complete simply connected manifolds under the assumption that the closures of leaves are compact orbifolds W of dimension at most 2. Explicit examples of the sphere \(S^{2n-1}\subset {\mathbb{C}}^ n\) with the flow \(f(z_ 1,...,z_ n;t)=(e^{i\lambda_ 1t}z_ 1,...,e^{i\lambda_ nt}z_ n)\) and the torus \({\mathbb{R}}^ n/{\mathbb{Z}}^ n\) permit to realize all models. A generalization for the case dim W\(>2\) is briefly mentioned.
Reviewer: J.Chrastina

MSC:
57R30 Foliations in differential topology; geometric theory
53C12 Foliations (differential geometric aspects)