Polar Foliations of Symmetric Spaces
نویسندگان
چکیده
منابع مشابه
Hyperpolar Homogeneous Foliations on Noncompact Symmetric Spaces
We introduce examples of hyperpolar actions on noncompact symmetric spaces that induce a regular foliation. We study some properties of these actions. Finally, we show that any hyperpolar action on a noncompact symmetric space that induces a regular foliation is one of these examples.
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Abstract. A foliation F on a Riemannian manifold M is hyperpolar if it admits a flat section, that is, a connected closed flat submanifold of M that intersects each leaf of F orthogonally. In this article we classify the hyperpolar homogeneous foliations on every Riemannian symmetric space M of noncompact type. These foliations are constructed as follows. Let Φ be an orthogonal subset of a set ...
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Let G be the group of k-points of a connected reductive k-group and H a symmetric subgroup associated to an involution σ of G. We prove a polar decomposition G = KAH for the symmetric space G/H over any local field k of characteristic not 2. Here K is a compact subset of G and A is a finite union of groups Ai which are the k-points of maximal (k, σ)-split tori, one for each H-conjugacy class. T...
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We construct interpolation operators for functions taking values in a symmetric space—a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized as a homogeneous space whose cosets have canonical representatives by virtue of the generalized polar decomposition—a generalization of the well-known factorizat...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2014
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-014-0279-2