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- W2042875401 abstract "We prove that if the normal distribution of a singular riemannian foliation is integrable, then each leaf of this normal distribution can be extended to be a complete immersed totally geodesic submanifold (called section) which meets every leaf orthogonally. In addition the set of regular points is open and dense in each section. This result generalizes a result of Boualem and solves a problem inspired by a remark of Palais and Terng and a work of Szenthe about polar actions. We also study the singular holonomy of a singular riemannian foliation with sections (s.r.f.s for short) and in particular the transverse orbit of the closure of each leaf. Furthermore we prove that the closure of the leaves of a s.r.f.s. on M form a partition of M which is a singular riemannian foliation. This result proves partially a conjecture of Molino." @default.
- W2042875401 created "2016-06-24" @default.
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- W2042875401 date "2006-04-01" @default.
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- W2042875401 title "Proofs of Conjectures about Singular Riemannian Foliations" @default.
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- W2042875401 doi "https://doi.org/10.1007/s10711-006-9073-0" @default.
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