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Collapsing regular Riemannian foliations with flat leaves (2403.11602v1)
Published 18 Mar 2024 in math.DG
Abstract: We present how to collapse a manifold equipped with a closed flat regular Riemannian foliation with leaves of positive dimension on a compact manifold, while keeping the sectional curvature uniformly bounded from above and below. From this deformation, we show that a closed flat regular Riemannian foliation with leaves of positive dimension on a compact simply-connected manifold is given by torus actions. This gives a geometric characterization of aspherical regular Riemannian foliations given by torus actions.
- Translated from the second Portuguese edition by Francis Flaherty.
- preprint, Cornell University.
- Seminar Bourbaki, Vol. 1983/84.
- https://anton-petrunin.github.io/papers/alexandrov/perelmanASWCBFB2+.pdf, last accessed 11 May 2023.
- URL: https://static1.squarespace.com/static/5994498937c5815907f7eb12/t/5998477717bffc656afd46e0/1503151996268/SRF+Lecture+Notes.pdf. Last accessed on 13 March 2023.