Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular Riemannian Foliations with Sections   In this paper we study singular riemannian foliations that have
sections,i.e., totally geodesic complete immersed submanifolds that meet each
leaf orthogonally and whose dimensions are the codimensions of the regular
leaves. We prove here that the restriction of the foliation to a slice of a
leaf is diffeomorphic to an isoparametric foliation on an open set of an
euclidian space. This result gives us local information about the singular
foliation and in particular about the singular stratification of the foliation.
It also allows us to describe the plaques of the foliation as level sets of a
transnormal map (a generalization of an isoparametric map). We also prove that
the regular leaves of a singular riemannian foliation with sections are locally
equifocal. We use this property to define a singular holonomy. Then we
establish some results about this singular holonomy and illustrate them with a
couple of examples.

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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci