caa a22 4500 463248066 CHVBK 20180405153332.0 cr unu---uuuuu 170326e20071001xx s 000 0 eng 10.1007/s10455-006-9052-6 doi (NATIONALLICENCE)springer-10.1007/s10455-006-9052-6 Singular riemannian foliations with sections, transnormal maps and basic forms [Elektronische Daten] [Marcos Alexandrino, Claudio Gorodski] A singular riemannian foliation $$\mathcal{F}$$ on a complete riemannian manifold M is said to admit sections if each regular point of M is contained in a complete totally geodesic immersed submanifold Σ that meets every leaf of $$\mathcal{F}$$ orthogonally and whose dimension is the codimension of the regular leaves of $$\mathcal{F}$$ . We prove that the algebra of basic forms of M relative to $$\mathcal{F}$$ is isomorphic to the algebra of those differential forms on Σ that are invariant under the generalized Weyl pseudogroup of Σ. This extends a result of Michor for polar actions. It follows from this result that the algebra of basic function is finitely generated if the sections are compact. We also prove that the leaves of $$\mathcal{F}$$ coincide with the level sets of a transnormal map (generalization of isoparametric map) if M is simply connected, the sections are flat and the leaves of $$\mathcal{F}$$ are compact. This result extends previous results due to Carter and West, Terng, and Heintze, Liu and Olmos. Springer Science + Business Media B.V., 2006 Singular riemannian foliations nationallicence Basic forms nationallicence Basic functions nationallicence Pseudogroups nationallicence Equifocal submanifolds nationallicence Polar actions nationallicence Isoparametric submanifolds nationallicence Alexandrino Marcos Instituto de Matemática e Estatística, Universidade de São Paulo (USP), Rua do Matão, 1010, Bloco A, 05508 090, São Paulo, Brazil aut Gorodski Claudio Instituto de Matemática e Estatística, Universidade de São Paulo (USP), Rua do Matão, 1010, Bloco A, 05508 090, São Paulo, Brazil aut Annals of Global Analysis and Geometry Springer Netherlands 32/3(2007-10-01), 209-223 0232-704X 32:3<209 2007 32 10455 https://doi.org/10.1007/s10455-006-9052-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10455-006-9052-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alexandrino Marcos Instituto de Matemática e Estatística, Universidade de São Paulo (USP), Rua do Matão, 1010, Bloco A, 05508 090, São Paulo, Brazil aut NATIONALLICENCE 700 1- Gorodski Claudio Instituto de Matemática e Estatística, Universidade de São Paulo (USP), Rua do Matão, 1010, Bloco A, 05508 090, São Paulo, Brazil aut NATIONALLICENCE 773 0- Annals of Global Analysis and Geometry Springer Netherlands 32/3(2007-10-01), 209-223 0232-704X 32:3<209 2007 32 10455 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer