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Théorèmes de slice et holonomie des feuilletages riemanniens singuliers. (Slice theorems and holonomy of singular Riemannian foliations). (French) Zbl 0625.57016
Soit (M,\({\mathcal F})\) un feuilletage riemannien sur une variété compacte; \(\bar {\mathcal F}\) est le feuilletage singulier défini par les adhérences des feuilles, (\=F,\({\mathcal F})\) le feuilletage induit sur une adhérence générique. On étudie le cas où (\=F,\({\mathcal F})\) n’a pas de champ transverse non trivial. Alors l’espace quotient \(W=M/\bar {\mathcal F}^ a \)une structure naturelle de variété de Sataké, de manière que la projection \(M\to W\) soit un morphisme de variétés de Sataké avec pliage autour des adhérences singulières.

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