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Feuilletages riemanniens singuliers transversalement intégrables. (French) Zbl 0854.53031
A singular Riemannian foliation is transversely integrable if on the open set of regular leaves, the distribution orthogonal to the regular leaves is completely integrable. Assuming that every leaf of a singular Riemannian foliation has compact closure, the author proves that through every point there exists a connected immersed submanifold which meets every leaf orthogonally. This proves a conjecture of R. S. Palais and C.-L. Terng [Critical point theory and submanifold geometry. Lect. Notes Math., 1353. Berlin etc.: Springer-Verlag (1988; Zbl 0658.49001)] concerning sections of compact group actions. The author also generalizes the decomposition theorem of R. A. Blumenthal and the reviewer [Ann. Inst. Fourier 33, No. 2, 183-198 (1983; Zbl 0509.57016)].
Reviewer: J.Hebda (St.Louis)

MSC:
53C12 Foliations (differential geometric aspects)
57R30 Foliations in differential topology; geometric theory
53C20 Global Riemannian geometry, including pinching
57S15 Compact Lie groups of differentiable transformations
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References:
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