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Geometric resolution of singular Riemannian foliations

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Abstract

We prove that an isometric action of a Lie group on a Riemannian manifold admits a resolution preserving the transverse geometry if and only if the action is infinitesimally polar. We provide applications concerning topological simplicity of several classes of isometric actions, including polar and variationally complete ones. All results are proven in the more general case of singular Riemannian foliations.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Bonn, Beringstr. 1, 53115, Bonn, Germany

    Alexander Lytchak

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  1. Alexander Lytchak
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Correspondence to Alexander Lytchak.

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The author was supported in part by the SFB 611 Singuläre Phänomene und Skalierung in mathematischen Modellen and by the MPI for mathematics in Bonn.

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Lytchak, A. Geometric resolution of singular Riemannian foliations. Geom Dedicata 149, 379–395 (2010). https://doi.org/10.1007/s10711-010-9488-5

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  • DOI: https://doi.org/10.1007/s10711-010-9488-5

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